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Sequence Series











































Marc first writes the perfect squares as a sequence

1,4,9,16,25,36,49,64,81,100...

After the number 1, he then alternates by making two terms negative followed
by leaving two terms negative.Marc's new sequence is:

1,-4,-9,16,25,-36,-49,64,81,-100...

What is the sum of the first 2011 terms in this new sequence?

Comments for Sequence Series

Click here to add your own comments

May 18, 2011
Sequence Series
by: Staff

--------------------------------

footnote (1) - Part XVIII


1961, , 3845521, 3847481
1962, , -3849444, -1963
1963, , -3853369, -3855332
1964, , 3857296, 1964
1965, , 3861225, 3863189
1966, , -3865156, -1967
1967, , -3869089, -3871056
1968, , 3873024, 1968
1969, , 3876961, 3878929
1970, , -3880900, -1971
1971, , -3884841, -3886812
1972, , 3888784, 1972
1973, , 3892729, 3894701
1974, , -3896676, -1975
1975, , -3900625, -3902600
1976, , 3904576, 1976
1977, , 3908529, 3910505
1978, , -3912484, -1979
1979, , -3916441, -3918420
1980, , 3920400, 1980
1981, , 3924361, 3926341
1982, , -3928324, -1983
1983, , -3932289, -3934272
1984, , 3936256, 1984
1985, , 3940225, 3942209
1986, , -3944196, -1987
1987, , -3948169, -3950156
1988, , 3952144, 1988
1989, , 3956121, 3958109
1990, , -3960100, -1991
1991, , -3964081, -3966072
1992, , 3968064, 1992
1993, , 3972049, 3974041
1994, , -3976036, -1995
1995, , -3980025, -3982020
1996, , 3984016, 1996
1997, , 3988009, 3990005
1998, , -3992004, -1999
1999, , -3996001, -3998000
2000, , 4000000, 2000
2001, , 4004001, 4006001
2002, , -4008004, -2003
2003, , -4012009, -4014012
2004, , 4016016, 2004
2005, , 4020025, 4022029
2006, , -4024036, -2007
2007, , -4028049, -4030056
2008, , 4032064, 2008
2009, , 4036081, 4038089
2010, , -4040100, -2011
2011, , -4044121, -4046132
2012, , 4048144, 2012
2013, , 4052169, 4054181
2014, , -4056196, -2015
2015, , -4060225, -4062240
2016, , 4064256, 2016
2017, , 4068289, 4070305
2018, , -4072324, -2019
2019, , -4076361, -4078380
2020, , 4080400, 2020
2021, , 4084441, 4086461
2022, , -4088484, -2023
2023, , -4092529, -4094552
2024, , 4096576, 2024
2025, , 4100625, 4102649
2026, , -4104676, -2027
2027, , -4108729, -4110756
2028, , 4112784, 2028
2029, , 4116841, 4118869
2030, , -4120900, -2031
2031, , -4124961, -4126992
2032, , 4129024, 2032
2033, , 4133089, 4135121
2034, , -4137156, -2035
2035, , -4141225, -4143260
2036, , 4145296, 2036
2037, , 4149369, 4151405
2038, , -4153444, -2039
2039, , -4157521, -4159560
2040, , 4161600, 2040
2041, , 4165681, 4167721
2042, , -4169764, -2043
2043, , -4173849, -4175892
2044, , 4177936, 2044
2045, , 4182025, 4184069
2046, , -4186116, -2047
2047, , -4190209, -4192256
2048, , 4194304, 2048
2049, , 4198401, 4200449
2050, , -4202500, -2051
2051, , -4206601, -4208652

May 18, 2011
Sequence Series
by: Staff

--------------------------------

footnote (1) - Part XVII



1861, , 3463321, 3465181
1862, , -3467044, -1863
1863, , -3470769, -3472632
1864, , 3474496, 1864
1865, , 3478225, 3480089
1866, , -3481956, -1867
1867, , -3485689, -3487556
1868, , 3489424, 1868
1869, , 3493161, 3495029
1870, , -3496900, -1871
1871, , -3500641, -3502512
1872, , 3504384, 1872
1873, , 3508129, 3510001
1874, , -3511876, -1875
1875, , -3515625, -3517500
1876, , 3519376, 1876
1877, , 3523129, 3525005
1878, , -3526884, -1879
1879, , -3530641, -3532520
1880, , 3534400, 1880
1881, , 3538161, 3540041
1882, , -3541924, -1883
1883, , -3545689, -3547572
1884, , 3549456, 1884
1885, , 3553225, 3555109
1886, , -3556996, -1887
1887, , -3560769, -3562656
1888, , 3564544, 1888
1889, , 3568321, 3570209
1890, , -3572100, -1891
1891, , -3575881, -3577772
1892, , 3579664, 1892
1893, , 3583449, 3585341
1894, , -3587236, -1895
1895, , -3591025, -3592920
1896, , 3594816, 1896
1897, , 3598609, 3600505
1898, , -3602404, -1899
1899, , -3606201, -3608100
1900, , 3610000, 1900
1901, , 3613801, 3615701
1902, , -3617604, -1903
1903, , -3621409, -3623312
1904, , 3625216, 1904
1905, , 3629025, 3630929
1906, , -3632836, -1907
1907, , -3636649, -3638556
1908, , 3640464, 1908
1909, , 3644281, 3646189
1910, , -3648100, -1911
1911, , -3651921, -3653832
1912, , 3655744, 1912
1913, , 3659569, 3661481
1914, , -3663396, -1915
1915, , -3667225, -3669140
1916, , 3671056, 1916
1917, , 3674889, 3676805
1918, , -3678724, -1919
1919, , -3682561, -3684480
1920, , 3686400, 1920
1921, , 3690241, 3692161
1922, , -3694084, -1923
1923, , -3697929, -3699852
1924, , 3701776, 1924
1925, , 3705625, 3707549
1926, , -3709476, -1927
1927, , -3713329, -3715256
1928, , 3717184, 1928
1929, , 3721041, 3722969
1930, , -3724900, -1931
1931, , -3728761, -3730692
1932, , 3732624, 1932
1933, , 3736489, 3738421
1934, , -3740356, -1935
1935, , -3744225, -3746160
1936, , 3748096, 1936
1937, , 3751969, 3753905
1938, , -3755844, -1939
1939, , -3759721, -3761660
1940, , 3763600, 1940
1941, , 3767481, 3769421
1942, , -3771364, -1943
1943, , -3775249, -3777192
1944, , 3779136, 1944
1945, , 3783025, 3784969
1946, , -3786916, -1947
1947, , -3790809, -3792756
1948, , 3794704, 1948
1949, , 3798601, 3800549
1950, , -3802500, -1951
1951, , -3806401, -3808352
1952, , 3810304, 1952
1953, , 3814209, 3816161
1954, , -3818116, -1955
1955, , -3822025, -3823980
1956, , 3825936, 1956
1957, , 3829849, 3831805
1958, , -3833764, -1959
1959, , -3837681, -3839640
1960, , 3841600, 1960
--------------------------------

May 18, 2011
Sequence Series
by: Staff

--------------------------------

footnote (1) - Part XVI


1751, , -3066001, -3067752
1752, , 3069504, 1752
1753, , 3073009, 3074761
1754, , -3076516, -1755
1755, , -3080025, -3081780
1756, , 3083536, 1756
1757, , 3087049, 3088805
1758, , -3090564, -1759
1759, , -3094081, -3095840
1760, , 3097600, 1760
1761, , 3101121, 3102881
1762, , -3104644, -1763
1763, , -3108169, -3109932
1764, , 3111696, 1764
1765, , 3115225, 3116989
1766, , -3118756, -1767
1767, , -3122289, -3124056
1768, , 3125824, 1768
1769, , 3129361, 3131129
1770, , -3132900, -1771
1771, , -3136441, -3138212
1772, , 3139984, 1772
1773, , 3143529, 3145301
1774, , -3147076, -1775
1775, , -3150625, -3152400
1776, , 3154176, 1776
1777, , 3157729, 3159505
1778, , -3161284, -1779
1779, , -3164841, -3166620
1780, , 3168400, 1780
1781, , 3171961, 3173741
1782, , -3175524, -1783
1783, , -3179089, -3180872
1784, , 3182656, 1784
1785, , 3186225, 3188009
1786, , -3189796, -1787
1787, , -3193369, -3195156
1788, , 3196944, 1788
1789, , 3200521, 3202309
1790, , -3204100, -1791
1791, , -3207681, -3209472
1792, , 3211264, 1792
1793, , 3214849, 3216641
1794, , -3218436, -1795
1795, , -3222025, -3223820
1796, , 3225616, 1796
1797, , 3229209, 3231005
1798, , -3232804, -1799
1799, , -3236401, -3238200
1800, , 3240000, 1800
1801, , 3243601, 3245401
1802, , -3247204, -1803
1803, , -3250809, -3252612
1804, , 3254416, 1804
1805, , 3258025, 3259829
1806, , -3261636, -1807
1807, , -3265249, -3267056
1808, , 3268864, 1808
1809, , 3272481, 3274289
1810, , -3276100, -1811
1811, , -3279721, -3281532
1812, , 3283344, 1812
1813, , 3286969, 3288781
1814, , -3290596, -1815
1815, , -3294225, -3296040
1816, , 3297856, 1816
1817, , 3301489, 3303305
1818, , -3305124, -1819
1819, , -3308761, -3310580
1820, , 3312400, 1820
1821, , 3316041, 3317861
1822, , -3319684, -1823
1823, , -3323329, -3325152
1824, , 3326976, 1824
1825, , 3330625, 3332449
1826, , -3334276, -1827
1827, , -3337929, -3339756
1828, , 3341584, 1828
1829, , 3345241, 3347069
1830, , -3348900, -1831
1831, , -3352561, -3354392
1832, , 3356224, 1832
1833, , 3359889, 3361721
1834, , -3363556, -1835
1835, , -3367225, -3369060
1836, , 3370896, 1836
1837, , 3374569, 3376405
1838, , -3378244, -1839
1839, , -3381921, -3383760
1840, , 3385600, 1840
1841, , 3389281, 3391121
1842, , -3392964, -1843
1843, , -3396649, -3398492
1844, , 3400336, 1844
1845, , 3404025, 3405869
1846, , -3407716, -1847
1847, , -3411409, -3413256
1848, , 3415104, 1848
1849, , 3418801, 3420649
1850, , -3422500, -1851
1851, , -3426201, -3428052
1852, , 3429904, 1852
1853, , 3433609, 3435461
1854, , -3437316, -1855
1855, , -3441025, -3442880
1856, , 3444736, 1856
1857, , 3448449, 3450305
1858, , -3452164, -1859
1859, , -3455881, -3457740
1860, , 3459600, 1860
--------------------------------

May 18, 2011
Sequence Series
by: Staff

--------------------------------

footnote (1) - Part XV


1641, , 2692881, 2694521
1642, , -2696164, -1643
1643, , -2699449, -2701092
1644, , 2702736, 1644
1645, , 2706025, 2707669
1646, , -2709316, -1647
1647, , -2712609, -2714256
1648, , 2715904, 1648
1649, , 2719201, 2720849
1650, , -2722500, -1651
1651, , -2725801, -2727452
1652, , 2729104, 1652
1653, , 2732409, 2734061
1654, , -2735716, -1655
1655, , -2739025, -2740680
1656, , 2742336, 1656
1657, , 2745649, 2747305
1658, , -2748964, -1659
1659, , -2752281, -2753940
1660, , 2755600, 1660
1661, , 2758921, 2760581
1662, , -2762244, -1663
1663, , -2765569, -2767232
1664, , 2768896, 1664
1665, , 2772225, 2773889
1666, , -2775556, -1667
1667, , -2778889, -2780556
1668, , 2782224, 1668
1669, , 2785561, 2787229
1670, , -2788900, -1671
1671, , -2792241, -2793912
1672, , 2795584, 1672
1673, , 2798929, 2800601
1674, , -2802276, -1675
1675, , -2805625, -2807300
1676, , 2808976, 1676
1677, , 2812329, 2814005
1678, , -2815684, -1679
1679, , -2819041, -2820720
1680, , 2822400, 1680
1681, , 2825761, 2827441
1682, , -2829124, -1683
1683, , -2832489, -2834172
1684, , 2835856, 1684
1685, , 2839225, 2840909
1686, , -2842596, -1687
1687, , -2845969, -2847656
1688, , 2849344, 1688
1689, , 2852721, 2854409
1690, , -2856100, -1691
1691, , -2859481, -2861172
1692, , 2862864, 1692
1693, , 2866249, 2867941
1694, , -2869636, -1695
1695, , -2873025, -2874720
1696, , 2876416, 1696
1697, , 2879809, 2881505
1698, , -2883204, -1699
1699, , -2886601, -2888300
1700, , 2890000, 1700
1701, , 2893401, 2895101
1702, , -2896804, -1703
1703, , -2900209, -2901912
1704, , 2903616, 1704
1705, , 2907025, 2908729
1706, , -2910436, -1707
1707, , -2913849, -2915556
1708, , 2917264, 1708
1709, , 2920681, 2922389
1710, , -2924100, -1711
1711, , -2927521, -2929232
1712, , 2930944, 1712
1713, , 2934369, 2936081
1714, , -2937796, -1715
1715, , -2941225, -2942940
1716, , 2944656, 1716
1717, , 2948089, 2949805
1718, , -2951524, -1719
1719, , -2954961, -2956680
1720, , 2958400, 1720
1721, , 2961841, 2963561
1722, , -2965284, -1723
1723, , -2968729, -2970452
1724, , 2972176, 1724
1725, , 2975625, 2977349
1726, , -2979076, -1727
1727, , -2982529, -2984256
1728, , 2985984, 1728
1729, , 2989441, 2991169
1730, , -2992900, -1731
1731, , -2996361, -2998092
1732, , 2999824, 1732
1733, , 3003289, 3005021
1734, , -3006756, -1735
1735, , -3010225, -3011960
1736, , 3013696, 1736
1737, , 3017169, 3018905
1738, , -3020644, -1739
1739, , -3024121, -3025860
1740, , 3027600, 1740
1741, , 3031081, 3032821
1742, , -3034564, -1743
1743, , -3038049, -3039792
1744, , 3041536, 1744
1745, , 3045025, 3046769
1746, , -3048516, -1747
1747, , -3052009, -3053756
1748, , 3055504, 1748
1749, , 3059001, 3060749
1750, , -3062500, -1751
--------------------------------

May 18, 2011
Sequence Series
by: Staff

--------------------------------

footnote (1) - Part XIV



1531, , -2343961, -2345492
1532, , 2347024, 1532
1533, , 2350089, 2351621
1534, , -2353156, -1535
1535, , -2356225, -2357760
1536, , 2359296, 1536
1537, , 2362369, 2363905
1538, , -2365444, -1539
1539, , -2368521, -2370060
1540, , 2371600, 1540
1541, , 2374681, 2376221
1542, , -2377764, -1543
1543, , -2380849, -2382392
1544, , 2383936, 1544
1545, , 2387025, 2388569
1546, , -2390116, -1547
1547, , -2393209, -2394756
1548, , 2396304, 1548
1549, , 2399401, 2400949
1550, , -2402500, -1551
1551, , -2405601, -2407152
1552, , 2408704, 1552
1553, , 2411809, 2413361
1554, , -2414916, -1555
1555, , -2418025, -2419580
1556, , 2421136, 1556
1557, , 2424249, 2425805
1558, , -2427364, -1559
1559, , -2430481, -2432040
1560, , 2433600, 1560
1561, , 2436721, 2438281
1562, , -2439844, -1563
1563, , -2442969, -2444532
1564, , 2446096, 1564
1565, , 2449225, 2450789
1566, , -2452356, -1567
1567, , -2455489, -2457056
1568, , 2458624, 1568
1569, , 2461761, 2463329
1570, , -2464900, -1571
1571, , -2468041, -2469612
1572, , 2471184, 1572
1573, , 2474329, 2475901
1574, , -2477476, -1575
1575, , -2480625, -2482200
1576, , 2483776, 1576
1577, , 2486929, 2488505
1578, , -2490084, -1579
1579, , -2493241, -2494820
1580, , 2496400, 1580
1581, , 2499561, 2501141
1582, , -2502724, -1583
1583, , -2505889, -2507472
1584, , 2509056, 1584
1585, , 2512225, 2513809
1586, , -2515396, -1587
1587, , -2518569, -2520156
1588, , 2521744, 1588
1589, , 2524921, 2526509
1590, , -2528100, -1591
1591, , -2531281, -2532872
1592, , 2534464, 1592
1593, , 2537649, 2539241
1594, , -2540836, -1595
1595, , -2544025, -2545620
1596, , 2547216, 1596
1597, , 2550409, 2552005
1598, , -2553604, -1599
1599, , -2556801, -2558400
1600, , 2560000, 1600
1601, , 2563201, 2564801
1602, , -2566404, -1603
1603, , -2569609, -2571212
1604, , 2572816, 1604
1605, , 2576025, 2577629
1606, , -2579236, -1607
1607, , -2582449, -2584056
1608, , 2585664, 1608
1609, , 2588881, 2590489
1610, , -2592100, -1611
1611, , -2595321, -2596932
1612, , 2598544, 1612
1613, , 2601769, 2603381
1614, , -2604996, -1615
1615, , -2608225, -2609840
1616, , 2611456, 1616
1617, , 2614689, 2616305
1618, , -2617924, -1619
1619, , -2621161, -2622780
1620, , 2624400, 1620
1621, , 2627641, 2629261
1622, , -2630884, -1623
1623, , -2634129, -2635752
1624, , 2637376, 1624
1625, , 2640625, 2642249
1626, , -2643876, -1627
1627, , -2647129, -2648756
1628, , 2650384, 1628
1629, , 2653641, 2655269
1630, , -2656900, -1631
1631, , -2660161, -2661792
1632, , 2663424, 1632
1633, , 2666689, 2668321
1634, , -2669956, -1635
1635, , -2673225, -2674860
1636, , 2676496, 1636
1637, , 2679769, 2681405
1638, , -2683044, -1639
1639, , -2686321, -2687960
1640, , 2689600, 1640
--------------------------------

May 18, 2011
Sequence Series
by: Staff

--------------------------------

footnote (1) - Part XIII


1421, , 2019241, 2020661
1422, , -2022084, -1423
1423, , -2024929, -2026352
1424, , 2027776, 1424
1425, , 2030625, 2032049
1426, , -2033476, -1427
1427, , -2036329, -2037756
1428, , 2039184, 1428
1429, , 2042041, 2043469
1430, , -2044900, -1431
1431, , -2047761, -2049192
1432, , 2050624, 1432
1433, , 2053489, 2054921
1434, , -2056356, -1435
1435, , -2059225, -2060660
1436, , 2062096, 1436
1437, , 2064969, 2066405
1438, , -2067844, -1439
1439, , -2070721, -2072160
1440, , 2073600, 1440
1441, , 2076481, 2077921
1442, , -2079364, -1443
1443, , -2082249, -2083692
1444, , 2085136, 1444
1445, , 2088025, 2089469
1446, , -2090916, -1447
1447, , -2093809, -2095256
1448, , 2096704, 1448
1449, , 2099601, 2101049
1450, , -2102500, -1451
1451, , -2105401, -2106852
1452, , 2108304, 1452
1453, , 2111209, 2112661
1454, , -2114116, -1455
1455, , -2117025, -2118480
1456, , 2119936, 1456
1457, , 2122849, 2124305
1458, , -2125764, -1459
1459, , -2128681, -2130140
1460, , 2131600, 1460
1461, , 2134521, 2135981
1462, , -2137444, -1463
1463, , -2140369, -2141832
1464, , 2143296, 1464
1465, , 2146225, 2147689
1466, , -2149156, -1467
1467, , -2152089, -2153556
1468, , 2155024, 1468
1469, , 2157961, 2159429
1470, , -2160900, -1471
1471, , -2163841, -2165312
1472, , 2166784, 1472
1473, , 2169729, 2171201
1474, , -2172676, -1475
1475, , -2175625, -2177100
1476, , 2178576, 1476
1477, , 2181529, 2183005
1478, , -2184484, -1479
1479, , -2187441, -2188920
1480, , 2190400, 1480
1481, , 2193361, 2194841
1482, , -2196324, -1483
1483, , -2199289, -2200772
1484, , 2202256, 1484
1485, , 2205225, 2206709
1486, , -2208196, -1487
1487, , -2211169, -2212656
1488, , 2214144, 1488
1489, , 2217121, 2218609
1490, , -2220100, -1491
1491, , -2223081, -2224572
1492, , 2226064, 1492
1493, , 2229049, 2230541
1494, , -2232036, -1495
1495, , -2235025, -2236520
1496, , 2238016, 1496
1497, , 2241009, 2242505
1498, , -2244004, -1499
1499, , -2247001, -2248500
1500, , 2250000, 1500
1501, , 2253001, 2254501
1502, , -2256004, -1503
1503, , -2259009, -2260512
1504, , 2262016, 1504
1505, , 2265025, 2266529
1506, , -2268036, -1507
1507, , -2271049, -2272556
1508, , 2274064, 1508
1509, , 2277081, 2278589
1510, , -2280100, -1511
1511, , -2283121, -2284632
1512, , 2286144, 1512
1513, , 2289169, 2290681
1514, , -2292196, -1515
1515, , -2295225, -2296740
1516, , 2298256, 1516
1517, , 2301289, 2302805
1518, , -2304324, -1519
1519, , -2307361, -2308880
1520, , 2310400, 1520
1521, , 2313441, 2314961
1522, , -2316484, -1523
1523, , -2319529, -2321052
1524, , 2322576, 1524
1525, , 2325625, 2327149
1526, , -2328676, -1527
1527, , -2331729, -2333256
1528, , 2334784, 1528
1529, , 2337841, 2339369
1530, , -2340900, -1531
--------------------------------

May 18, 2011
Sequence Series
by: Staff

--------------------------------

footnote (1) - Part XII


1311, , -1718721, -1720032
1312, , 1721344, 1312
1313, , 1723969, 1725281
1314, , -1726596, -1315
1315, , -1729225, -1730540
1316, , 1731856, 1316
1317, , 1734489, 1735805
1318, , -1737124, -1319
1319, , -1739761, -1741080
1320, , 1742400, 1320
1321, , 1745041, 1746361
1322, , -1747684, -1323
1323, , -1750329, -1751652
1324, , 1752976, 1324
1325, , 1755625, 1756949
1326, , -1758276, -1327
1327, , -1760929, -1762256
1328, , 1763584, 1328
1329, , 1766241, 1767569
1330, , -1768900, -1331
1331, , -1771561, -1772892
1332, , 1774224, 1332
1333, , 1776889, 1778221
1334, , -1779556, -1335
1335, , -1782225, -1783560
1336, , 1784896, 1336
1337, , 1787569, 1788905
1338, , -1790244, -1339
1339, , -1792921, -1794260
1340, , 1795600, 1340
1341, , 1798281, 1799621
1342, , -1800964, -1343
1343, , -1803649, -1804992
1344, , 1806336, 1344
1345, , 1809025, 1810369
1346, , -1811716, -1347
1347, , -1814409, -1815756
1348, , 1817104, 1348
1349, , 1819801, 1821149
1350, , -1822500, -1351
1351, , -1825201, -1826552
1352, , 1827904, 1352
1353, , 1830609, 1831961
1354, , -1833316, -1355
1355, , -1836025, -1837380
1356, , 1838736, 1356
1357, , 1841449, 1842805
1358, , -1844164, -1359
1359, , -1846881, -1848240
1360, , 1849600, 1360
1361, , 1852321, 1853681
1362, , -1855044, -1363
1363, , -1857769, -1859132
1364, , 1860496, 1364
1365, , 1863225, 1864589
1366, , -1865956, -1367
1367, , -1868689, -1870056
1368, , 1871424, 1368
1369, , 1874161, 1875529
1370, , -1876900, -1371
1371, , -1879641, -1881012
1372, , 1882384, 1372
1373, , 1885129, 1886501
1374, , -1887876, -1375
1375, , -1890625, -1892000
1376, , 1893376, 1376
1377, , 1896129, 1897505
1378, , -1898884, -1379
1379, , -1901641, -1903020
1380, , 1904400, 1380
1381, , 1907161, 1908541
1382, , -1909924, -1383
1383, , -1912689, -1914072
1384, , 1915456, 1384
1385, , 1918225, 1919609
1386, , -1920996, -1387
1387, , -1923769, -1925156
1388, , 1926544, 1388
1389, , 1929321, 1930709
1390, , -1932100, -1391
1391, , -1934881, -1936272
1392, , 1937664, 1392
1393, , 1940449, 1941841
1394, , -1943236, -1395
1395, , -1946025, -1947420
1396, , 1948816, 1396
1397, , 1951609, 1953005
1398, , -1954404, -1399
1399, , -1957201, -1958600
1400, , 1960000, 1400
1401, , 1962801, 1964201
1402, , -1965604, -1403
1403, , -1968409, -1969812
1404, , 1971216, 1404
1405, , 1974025, 1975429
1406, , -1976836, -1407
1407, , -1979649, -1981056
1408, , 1982464, 1408
1409, , 1985281, 1986689
1410, , -1988100, -1411
1411, , -1990921, -1992332
1412, , 1993744, 1412
1413, , 1996569, 1997981
1414, , -1999396, -1415
1415, , -2002225, -2003640
1416, , 2005056, 1416
1417, , 2007889, 2009305
1418, , -2010724, -1419
1419, , -2013561, -2014980
1420, , 2016400, 1420
--------------------------------

May 18, 2011
Sequence Series
by: Staff

--------------------------------

footnote (1) - Part XI

1201, , 1442401, 1443601
1202, , -1444804, -1203
1203, , -1447209, -1448412
1204, , 1449616, 1204
1205, , 1452025, 1453229
1206, , -1454436, -1207
1207, , -1456849, -1458056
1208, , 1459264, 1208
1209, , 1461681, 1462889
1210, , -1464100, -1211
1211, , -1466521, -1467732
1212, , 1468944, 1212
1213, , 1471369, 1472581
1214, , -1473796, -1215
1215, , -1476225, -1477440
1216, , 1478656, 1216
1217, , 1481089, 1482305
1218, , -1483524, -1219
1219, , -1485961, -1487180
1220, , 1488400, 1220
1221, , 1490841, 1492061
1222, , -1493284, -1223
1223, , -1495729, -1496952
1224, , 1498176, 1224
1225, , 1500625, 1501849
1226, , -1503076, -1227
1227, , -1505529, -1506756
1228, , 1507984, 1228
1229, , 1510441, 1511669
1230, , -1512900, -1231
1231, , -1515361, -1516592
1232, , 1517824, 1232
1233, , 1520289, 1521521
1234, , -1522756, -1235
1235, , -1525225, -1526460
1236, , 1527696, 1236
1237, , 1530169, 1531405
1238, , -1532644, -1239
1239, , -1535121, -1536360
1240, , 1537600, 1240
1241, , 1540081, 1541321
1242, , -1542564, -1243
1243, , -1545049, -1546292
1244, , 1547536, 1244
1245, , 1550025, 1551269
1246, , -1552516, -1247
1247, , -1555009, -1556256
1248, , 1557504, 1248
1249, , 1560001, 1561249
1250, , -1562500, -1251
1251, , -1565001, -1566252
1252, , 1567504, 1252
1253, , 1570009, 1571261
1254, , -1572516, -1255
1255, , -1575025, -1576280
1256, , 1577536, 1256
1257, , 1580049, 1581305
1258, , -1582564, -1259
1259, , -1585081, -1586340
1260, , 1587600, 1260
1261, , 1590121, 1591381
1262, , -1592644, -1263
1263, , -1595169, -1596432
1264, , 1597696, 1264
1265, , 1600225, 1601489
1266, , -1602756, -1267
1267, , -1605289, -1606556
1268, , 1607824, 1268
1269, , 1610361, 1611629
1270, , -1612900, -1271
1271, , -1615441, -1616712
1272, , 1617984, 1272
1273, , 1620529, 1621801
1274, , -1623076, -1275
1275, , -1625625, -1626900
1276, , 1628176, 1276
1277, , 1630729, 1632005
1278, , -1633284, -1279
1279, , -1635841, -1637120
1280, , 1638400, 1280
1281, , 1640961, 1642241
1282, , -1643524, -1283
1283, , -1646089, -1647372
1284, , 1648656, 1284
1285, , 1651225, 1652509
1286, , -1653796, -1287
1287, , -1656369, -1657656
1288, , 1658944, 1288
1289, , 1661521, 1662809
1290, , -1664100, -1291
1291, , -1666681, -1667972
1292, , 1669264, 1292
1293, , 1671849, 1673141
1294, , -1674436, -1295
1295, , -1677025, -1678320
1296, , 1679616, 1296
1297, , 1682209, 1683505
1298, , -1684804, -1299
1299, , -1687401, -1688700
1300, , 1690000, 1300
1301, , 1692601, 1693901
1302, , -1695204, -1303
1303, , -1697809, -1699112
1304, , 1700416, 1304
1305, , 1703025, 1704329
1306, , -1705636, -1307
1307, , -1708249, -1709556
1308, , 1710864, 1308
1309, , 1713481, 1714789
1310, , -1716100, -1311
--------------------------------

May 18, 2011
Sequence Series
by: Staff

--------------------------------

footnote (1) - Part X


1101, , 1212201, 1213301
1102, , -1214404, -1103
1103, , -1216609, -1217712
1104, , 1218816, 1104
1105, , 1221025, 1222129
1106, , -1223236, -1107
1107, , -1225449, -1226556
1108, , 1227664, 1108
1109, , 1229881, 1230989
1110, , -1232100, -1111
1111, , -1234321, -1235432
1112, , 1236544, 1112
1113, , 1238769, 1239881
1114, , -1240996, -1115
1115, , -1243225, -1244340
1116, , 1245456, 1116
1117, , 1247689, 1248805
1118, , -1249924, -1119
1119, , -1252161, -1253280
1120, , 1254400, 1120
1121, , 1256641, 1257761
1122, , -1258884, -1123
1123, , -1261129, -1262252
1124, , 1263376, 1124
1125, , 1265625, 1266749
1126, , -1267876, -1127
1127, , -1270129, -1271256
1128, , 1272384, 1128
1129, , 1274641, 1275769
1130, , -1276900, -1131
1131, , -1279161, -1280292
1132, , 1281424, 1132
1133, , 1283689, 1284821
1134, , -1285956, -1135
1135, , -1288225, -1289360
1136, , 1290496, 1136
1137, , 1292769, 1293905
1138, , -1295044, -1139
1139, , -1297321, -1298460
1140, , 1299600, 1140
1141, , 1301881, 1303021
1142, , -1304164, -1143
1143, , -1306449, -1307592
1144, , 1308736, 1144
1145, , 1311025, 1312169
1146, , -1313316, -1147
1147, , -1315609, -1316756
1148, , 1317904, 1148
1149, , 1320201, 1321349
1150, , -1322500, -1151
1151, , -1324801, -1325952
1152, , 1327104, 1152
1153, , 1329409, 1330561
1154, , -1331716, -1155
1155, , -1334025, -1335180
1156, , 1336336, 1156
1157, , 1338649, 1339805
1158, , -1340964, -1159
1159, , -1343281, -1344440
1160, , 1345600, 1160
1161, , 1347921, 1349081
1162, , -1350244, -1163
1163, , -1352569, -1353732
1164, , 1354896, 1164
1165, , 1357225, 1358389
1166, , -1359556, -1167
1167, , -1361889, -1363056
1168, , 1364224, 1168
1169, , 1366561, 1367729
1170, , -1368900, -1171
1171, , -1371241, -1372412
1172, , 1373584, 1172
1173, , 1375929, 1377101
1174, , -1378276, -1175
1175, , -1380625, -1381800
1176, , 1382976, 1176
1177, , 1385329, 1386505
1178, , -1387684, -1179
1179, , -1390041, -1391220
1180, , 1392400, 1180
1181, , 1394761, 1395941
1182, , -1397124, -1183
1183, , -1399489, -1400672
1184, , 1401856, 1184
1185, , 1404225, 1405409
1186, , -1406596, -1187
1187, , -1408969, -1410156
1188, , 1411344, 1188
1189, , 1413721, 1414909
1190, , -1416100, -1191
1191, , -1418481, -1419672
1192, , 1420864, 1192
1193, , 1423249, 1424441
1194, , -1425636, -1195
1195, , -1428025, -1429220
1196, , 1430416, 1196
1197, , 1432809, 1434005
1198, , -1435204, -1199
1199, , -1437601, -1438800
1200, , 1440000, 1200
--------------------------------

May 18, 2011
Sequence Series
by: Staff

--------------------------------

footnote (1) - Part IX

1001, , 1002001, 1003001
1002, , -1004004, -1003
1003, , -1006009, -1007012
1004, , 1008016, 1004
1005, , 1010025, 1011029
1006, , -1012036, -1007
1007, , -1014049, -1015056
1008, , 1016064, 1008
1009, , 1018081, 1019089
1010, , -1020100, -1011
1011, , -1022121, -1023132
1012, , 1024144, 1012
1013, , 1026169, 1027181
1014, , -1028196, -1015
1015, , -1030225, -1031240
1016, , 1032256, 1016
1017, , 1034289, 1035305
1018, , -1036324, -1019
1019, , -1038361, -1039380
1020, , 1040400, 1020
1021, , 1042441, 1043461
1022, , -1044484, -1023
1023, , -1046529, -1047552
1024, , 1048576, 1024
1025, , 1050625, 1051649
1026, , -1052676, -1027
1027, , -1054729, -1055756
1028, , 1056784, 1028
1029, , 1058841, 1059869
1030, , -1060900, -1031
1031, , -1062961, -1063992
1032, , 1065024, 1032
1033, , 1067089, 1068121
1034, , -1069156, -1035
1035, , -1071225, -1072260
1036, , 1073296, 1036
1037, , 1075369, 1076405
1038, , -1077444, -1039
1039, , -1079521, -1080560
1040, , 1081600, 1040
1041, , 1083681, 1084721
1042, , -1085764, -1043
1043, , -1087849, -1088892
1044, , 1089936, 1044
1045, , 1092025, 1093069
1046, , -1094116, -1047
1047, , -1096209, -1097256
1048, , 1098304, 1048
1049, , 1100401, 1101449
1050, , -1102500, -1051
1051, , -1104601, -1105652
1052, , 1106704, 1052
1053, , 1108809, 1109861
1054, , -1110916, -1055
1055, , -1113025, -1114080
1056, , 1115136, 1056
1057, , 1117249, 1118305
1058, , -1119364, -1059
1059, , -1121481, -1122540
1060, , 1123600, 1060
1061, , 1125721, 1126781
1062, , -1127844, -1063
1063, , -1129969, -1131032
1064, , 1132096, 1064
1065, , 1134225, 1135289
1066, , -1136356, -1067
1067, , -1138489, -1139556
1068, , 1140624, 1068
1069, , 1142761, 1143829
1070, , -1144900, -1071
1071, , -1147041, -1148112
1072, , 1149184, 1072
1073, , 1151329, 1152401
1074, , -1153476, -1075
1075, , -1155625, -1156700
1076, , 1157776, 1076
1077, , 1159929, 1161005
1078, , -1162084, -1079
1079, , -1164241, -1165320
1080, , 1166400, 1080
1081, , 1168561, 1169641
1082, , -1170724, -1083
1083, , -1172889, -1173972
1084, , 1175056, 1084
1085, , 1177225, 1178309
1086, , -1179396, -1087
1087, , -1181569, -1182656
1088, , 1183744, 1088
1089, , 1185921, 1187009
1090, , -1188100, -1091
1091, , -1190281, -1191372
1092, , 1192464, 1092
1093, , 1194649, 1195741
1094, , -1196836, -1095
1095, , -1199025, -1200120
1096, , 1201216, 1096
1097, , 1203409, 1204505
1098, , -1205604, -1099
1099, , -1207801, -1208900
1100, , 1210000, 1100
--------------------------------

May 18, 2011
Sequence Series
by: Staff

--------------------------------

footnote (1) - Part VIII


881, , 776161, 777041
882, , -777924, -883
883, , -779689, -780572
884, , 781456, 884
885, , 783225, 784109
886, , -784996, -887
887, , -786769, -787656
888, , 788544, 888
889, , 790321, 791209
890, , -792100, -891
891, , -793881, -794772
892, , 795664, 892
893, , 797449, 798341
894, , -799236, -895
895, , -801025, -801920
896, , 802816, 896
897, , 804609, 805505
898, , -806404, -899
899, , -808201, -809100
900, , 810000, 900
901, , 811801, 812701
902, , -813604, -903
903, , -815409, -816312
904, , 817216, 904
905, , 819025, 819929
906, , -820836, -907
907, , -822649, -823556
908, , 824464, 908
909, , 826281, 827189
910, , -828100, -911
911, , -829921, -830832
912, , 831744, 912
913, , 833569, 834481
914, , -835396, -915
915, , -837225, -838140
916, , 839056, 916
917, , 840889, 841805
918, , -842724, -919
919, , -844561, -845480
920, , 846400, 920
921, , 848241, 849161
922, , -850084, -923
923, , -851929, -852852
924, , 853776, 924
925, , 855625, 856549
926, , -857476, -927
927, , -859329, -860256
928, , 861184, 928
929, , 863041, 863969
930, , -864900, -931
931, , -866761, -867692
932, , 868624, 932
933, , 870489, 871421
934, , -872356, -935
935, , -874225, -875160
936, , 876096, 936
937, , 877969, 878905
938, , -879844, -939
939, , -881721, -882660
940, , 883600, 940
941, , 885481, 886421
942, , -887364, -943
943, , -889249, -890192
944, , 891136, 944
945, , 893025, 893969
946, , -894916, -947
947, , -896809, -897756
948, , 898704, 948
949, , 900601, 901549
950, , -902500, -951
951, , -904401, -905352
952, , 906304, 952
953, , 908209, 909161
954, , -910116, -955
955, , -912025, -912980
956, , 913936, 956
957, , 915849, 916805
958, , -917764, -959
959, , -919681, -920640
960, , 921600, 960
961, , 923521, 924481
962, , -925444, -963
963, , -927369, -928332
964, , 929296, 964
965, , 931225, 932189
966, , -933156, -967
967, , -935089, -936056
968, , 937024, 968
969, , 938961, 939929
970, , -940900, -971
971, , -942841, -943812
972, , 944784, 972
973, , 946729, 947701
974, , -948676, -975
975, , -950625, -951600
976, , 952576, 976
977, , 954529, 955505
978, , -956484, -979
979, , -958441, -959420
980, , 960400, 980
981, , 962361, 963341
982, , -964324, -983
983, , -966289, -967272
984, , 968256, 984
985, , 970225, 971209
986, , -972196, -987
987, , -974169, -975156
988, , 976144, 988
989, , 978121, 979109
990, , -980100, -991
991, , -982081, -983072
992, , 984064, 992
993, , 986049, 987041
994, , -988036, -995
995, , -990025, -991020
996, , 992016, 996
997, , 994009, 995005
998, , -996004, -999
999, , -998001, -999000
1000, , 1000000, 1000
--------------------------------

May 18, 2011
Sequence Series
by: Staff

--------------------------------

footnote (1) - Part VII

761, , 579121, 579881
762, , -580644, -763
763, , -582169, -582932
764, , 583696, 764
765, , 585225, 585989
766, , -586756, -767
767, , -588289, -589056
768, , 589824, 768
769, , 591361, 592129
770, , -592900, -771
771, , -594441, -595212
772, , 595984, 772
773, , 597529, 598301
774, , -599076, -775
775, , -600625, -601400
776, , 602176, 776
777, , 603729, 604505
778, , -605284, -779
779, , -606841, -607620
780, , 608400, 780
781, , 609961, 610741
782, , -611524, -783
783, , -613089, -613872
784, , 614656, 784
785, , 616225, 617009
786, , -617796, -787
787, , -619369, -620156
788, , 620944, 788
789, , 622521, 623309
790, , -624100, -791
791, , -625681, -626472
792, , 627264, 792
793, , 628849, 629641
794, , -630436, -795
795, , -632025, -632820
796, , 633616, 796
797, , 635209, 636005
798, , -636804, -799
799, , -638401, -639200
800, , 640000, 800
801, , 641601, 642401
802, , -643204, -803
803, , -644809, -645612
804, , 646416, 804
805, , 648025, 648829
806, , -649636, -807
807, , -651249, -652056
808, , 652864, 808
809, , 654481, 655289
810, , -656100, -811
811, , -657721, -658532
812, , 659344, 812
813, , 660969, 661781
814, , -662596, -815
815, , -664225, -665040
816, , 665856, 816
817, , 667489, 668305
818, , -669124, -819
819, , -670761, -671580
820, , 672400, 820
821, , 674041, 674861
822, , -675684, -823
823, , -677329, -678152
824, , 678976, 824
825, , 680625, 681449
826, , -682276, -827
827, , -683929, -684756
828, , 685584, 828
829, , 687241, 688069
830, , -688900, -831
831, , -690561, -691392
832, , 692224, 832
833, , 693889, 694721
834, , -695556, -835
835, , -697225, -698060
836, , 698896, 836
837, , 700569, 701405
838, , -702244, -839
839, , -703921, -704760
840, , 705600, 840
841, , 707281, 708121
842, , -708964, -843
843, , -710649, -711492
844, , 712336, 844
845, , 714025, 714869
846, , -715716, -847
847, , -717409, -718256
848, , 719104, 848
849, , 720801, 721649
850, , -722500, -851
851, , -724201, -725052
852, , 725904, 852
853, , 727609, 728461
854, , -729316, -855
855, , -731025, -731880
856, , 732736, 856
857, , 734449, 735305
858, , -736164, -859
859, , -737881, -738740
860, , 739600, 860
861, , 741321, 742181
862, , -743044, -863
863, , -744769, -745632
864, , 746496, 864
865, , 748225, 749089
866, , -749956, -867
867, , -751689, -752556
868, , 753424, 868
869, , 755161, 756029
870, , -756900, -871
871, , -758641, -759512
872, , 760384, 872
873, , 762129, 763001
874, , -763876, -875
875, , -765625, -766500
876, , 767376, 876
877, , 769129, 770005
878, , -770884, -879
879, , -772641, -773520
880, , 774400, 880
--------------------------------

May 18, 2011
Sequence Series
by: Staff

--------------------------------

footnote (1) - Part VI

641, , 410881, 411521
642, , -412164, -643
643, , -413449, -414092
644, , 414736, 644
645, , 416025, 416669
646, , -417316, -647
647, , -418609, -419256
648, , 419904, 648
649, , 421201, 421849
650, , -422500, -651
651, , -423801, -424452
652, , 425104, 652
653, , 426409, 427061
654, , -427716, -655
655, , -429025, -429680
656, , 430336, 656
657, , 431649, 432305
658, , -432964, -659
659, , -434281, -434940
660, , 435600, 660
661, , 436921, 437581
662, , -438244, -663
663, , -439569, -440232
664, , 440896, 664
665, , 442225, 442889
666, , -443556, -667
667, , -444889, -445556
668, , 446224, 668
669, , 447561, 448229
670, , -448900, -671
671, , -450241, -450912
672, , 451584, 672
673, , 452929, 453601
674, , -454276, -675
675, , -455625, -456300
676, , 456976, 676
677, , 458329, 459005
678, , -459684, -679
679, , -461041, -461720
680, , 462400, 680
681, , 463761, 464441
682, , -465124, -683
683, , -466489, -467172
684, , 467856, 684
685, , 469225, 469909
686, , -470596, -687
687, , -471969, -472656
688, , 473344, 688
689, , 474721, 475409
690, , -476100, -691
691, , -477481, -478172
692, , 478864, 692
693, , 480249, 480941
694, , -481636, -695
695, , -483025, -483720
696, , 484416, 696
697, , 485809, 486505
698, , -487204, -699
699, , -488601, -489300
700, , 490000, 700
701, , 491401, 492101
702, , -492804, -703
703, , -494209, -494912
704, , 495616, 704
705, , 497025, 497729
706, , -498436, -707
707, , -499849, -500556
708, , 501264, 708
709, , 502681, 503389
710, , -504100, -711
711, , -505521, -506232
712, , 506944, 712
713, , 508369, 509081
714, , -509796, -715
715, , -511225, -511940
716, , 512656, 716
717, , 514089, 514805
718, , -515524, -719
719, , -516961, -517680
720, , 518400, 720
721, , 519841, 520561
722, , -521284, -723
723, , -522729, -523452
724, , 524176, 724
725, , 525625, 526349
726, , -527076, -727
727, , -528529, -529256
728, , 529984, 728
729, , 531441, 532169
730, , -532900, -731
731, , -534361, -535092
732, , 535824, 732
733, , 537289, 538021
734, , -538756, -735
735, , -540225, -540960
736, , 541696, 736
737, , 543169, 543905
738, , -544644, -739
739, , -546121, -546860
740, , 547600, 740
741, , 549081, 549821
742, , -550564, -743
743, , -552049, -552792
744, , 553536, 744
745, , 555025, 555769
746, , -556516, -747
747, , -558009, -558756
748, , 559504, 748
749, , 561001, 561749
750, , -562500, -751
751, , -564001, -564752
752, , 565504, 752
753, , 567009, 567761
754, , -568516, -755
755, , -570025, -570780
756, , 571536, 756
757, , 573049, 573805
758, , -574564, -759
759, , -576081, -576840
760, , 577600, 760
--------------------------------

May 18, 2011
Sequence Series
by: Staff

--------------------------------

footnote (1) - Part V

521, , 271441, 271961
522, , -272484, -523
523, , -273529, -274052
524, , 274576, 524
525, , 275625, 276149
526, , -276676, -527
527, , -277729, -278256
528, , 278784, 528
529, , 279841, 280369
530, , -280900, -531
531, , -281961, -282492
532, , 283024, 532
533, , 284089, 284621
534, , -285156, -535
535, , -286225, -286760
536, , 287296, 536
537, , 288369, 288905
538, , -289444, -539
539, , -290521, -291060
540, , 291600, 540
541, , 292681, 293221
542, , -293764, -543
543, , -294849, -295392
544, , 295936, 544
545, , 297025, 297569
546, , -298116, -547
547, , -299209, -299756
548, , 300304, 548
549, , 301401, 301949
550, , -302500, -551
551, , -303601, -304152
552, , 304704, 552
553, , 305809, 306361
554, , -306916, -555
555, , -308025, -308580
556, , 309136, 556
557, , 310249, 310805
558, , -311364, -559
559, , -312481, -313040
560, , 313600, 560
561, , 314721, 315281
562, , -315844, -563
563, , -316969, -317532
564, , 318096, 564
565, , 319225, 319789
566, , -320356, -567
567, , -321489, -322056
568, , 322624, 568
569, , 323761, 324329
570, , -324900, -571
571, , -326041, -326612
572, , 327184, 572
573, , 328329, 328901
574, , -329476, -575
575, , -330625, -331200
576, , 331776, 576
577, , 332929, 333505
578, , -334084, -579
579, , -335241, -335820
580, , 336400, 580
581, , 337561, 338141
582, , -338724, -583
583, , -339889, -340472
584, , 341056, 584
585, , 342225, 342809
586, , -343396, -587
587, , -344569, -345156
588, , 345744, 588
589, , 346921, 347509
590, , -348100, -591
591, , -349281, -349872
592, , 350464, 592
593, , 351649, 352241
594, , -352836, -595
595, , -354025, -354620
596, , 355216, 596
597, , 356409, 357005
598, , -357604, -599
599, , -358801, -359400
600, , 360000, 600
601, , 361201, 361801
602, , -362404, -603
603, , -363609, -364212
604, , 364816, 604
605, , 366025, 366629
606, , -367236, -607
607, , -368449, -369056
608, , 369664, 608
609, , 370881, 371489
610, , -372100, -611
611, , -373321, -373932
612, , 374544, 612
613, , 375769, 376381
614, , -376996, -615
615, , -378225, -378840
616, , 379456, 616
617, , 380689, 381305
618, , -381924, -619
619, , -383161, -383780
620, , 384400, 620
621, , 385641, 386261
622, , -386884, -623
623, , -388129, -388752
624, , 389376, 624
625, , 390625, 391249
626, , -391876, -627
627, , -393129, -393756
628, , 394384, 628
629, , 395641, 396269
630, , -396900, -631
631, , -398161, -398792
632, , 399424, 632
633, , 400689, 401321
634, , -401956, -635
635, , -403225, -403860
636, , 404496, 636
637, , 405769, 406405
638, , -407044, -639
639, , -408321, -408960
640, , 409600, 640
--------------------------------

May 18, 2011
Sequence Series
by: Staff

--------------------------------

footnote (1) - Part IV


401, , 160801, 161201
402, , -161604, -403
403, , -162409, -162812
404, , 163216, 404
405, , 164025, 164429
406, , -164836, -407
407, , -165649, -166056
408, , 166464, 408
409, , 167281, 167689
410, , -168100, -411
411, , -168921, -169332
412, , 169744, 412
413, , 170569, 170981
414, , -171396, -415
415, , -172225, -172640
416, , 173056, 416
417, , 173889, 174305
418, , -174724, -419
419, , -175561, -175980
420, , 176400, 420
421, , 177241, 177661
422, , -178084, -423
423, , -178929, -179352
424, , 179776, 424
425, , 180625, 181049
426, , -181476, -427
427, , -182329, -182756
428, , 183184, 428
429, , 184041, 184469
430, , -184900, -431
431, , -185761, -186192
432, , 186624, 432
433, , 187489, 187921
434, , -188356, -435
435, , -189225, -189660
436, , 190096, 436
437, , 190969, 191405
438, , -191844, -439
439, , -192721, -193160
440, , 193600, 440
441, , 194481, 194921
442, , -195364, -443
443, , -196249, -196692
444, , 197136, 444
445, , 198025, 198469
446, , -198916, -447
447, , -199809, -200256
448, , 200704, 448
449, , 201601, 202049
450, , -202500, -451
451, , -203401, -203852
452, , 204304, 452
453, , 205209, 205661
454, , -206116, -455
455, , -207025, -207480
456, , 207936, 456
457, , 208849, 209305
458, , -209764, -459
459, , -210681, -211140
460, , 211600, 460
461, , 212521, 212981
462, , -213444, -463
463, , -214369, -214832
464, , 215296, 464
465, , 216225, 216689
466, , -217156, -467
467, , -218089, -218556
468, , 219024, 468
469, , 219961, 220429
470, , -220900, -471
471, , -221841, -222312
472, , 222784, 472
473, , 223729, 224201
474, , -224676, -475
475, , -225625, -226100
476, , 226576, 476
477, , 227529, 228005
478, , -228484, -479
479, , -229441, -229920
480, , 230400, 480
481, , 231361, 231841
482, , -232324, -483
483, , -233289, -233772
484, , 234256, 484
485, , 235225, 235709
486, , -236196, -487
487, , -237169, -237656
488, , 238144, 488
489, , 239121, 239609
490, , -240100, -491
491, , -241081, -241572
492, , 242064, 492
493, , 243049, 243541
494, , -244036, -495
495, , -245025, -245520
496, , 246016, 496
497, , 247009, 247505
498, , -248004, -499
499, , -249001, -249500
500, , 250000, 500
501, , 251001, 251501
502, , -252004, -503
503, , -253009, -253512
504, , 254016, 504
505, , 255025, 255529
506, , -256036, -507
507, , -257049, -257556
508, , 258064, 508
509, , 259081, 259589
510, , -260100, -511
511, , -261121, -261632
512, , 262144, 512
513, , 263169, 263681
514, , -264196, -515
515, , -265225, -265740
516, , 266256, 516
517, , 267289, 267805
518, , -268324, -519
519, , -269361, -269880
520, , 270400, 520
--------------------------------

May 18, 2011
Sequence Series
by: Staff

--------------------------------

footnote (1) - Part III


281, , 78961, 79241
282, , -79524, -283
283, , -80089, -80372
284, , 80656, 284
285, , 81225, 81509
286, , -81796, -287
287, , -82369, -82656
288, , 82944, 288
289, , 83521, 83809
290, , -84100, -291
291, , -84681, -84972
292, , 85264, 292
293, , 85849, 86141
294, , -86436, -295
295, , -87025, -87320
296, , 87616, 296
297, , 88209, 88505
298, , -88804, -299
299, , -89401, -89700
300, , 90000, 300
301, , 90601, 90901
302, , -91204, -303
303, , -91809, -92112
304, , 92416, 304
305, , 93025, 93329
306, , -93636, -307
307, , -94249, -94556
308, , 94864, 308
309, , 95481, 95789
310, , -96100, -311
311, , -96721, -97032
312, , 97344, 312
313, , 97969, 98281
314, , -98596, -315
315, , -99225, -99540
316, , 99856, 316
317, , 100489, 100805
318, , -101124, -319
319, , -101761, -102080
320, , 102400, 320
321, , 103041, 103361
322, , -103684, -323
323, , -104329, -104652
324, , 104976, 324
325, , 105625, 105949
326, , -106276, -327
327, , -106929, -107256
328, , 107584, 328
329, , 108241, 108569
330, , -108900, -331
331, , -109561, -109892
332, , 110224, 332
333, , 110889, 111221
334, , -111556, -335
335, , -112225, -112560
336, , 112896, 336
337, , 113569, 113905
338, , -114244, -339
339, , -114921, -115260
340, , 115600, 340
341, , 116281, 116621
342, , -116964, -343
343, , -117649, -117992
344, , 118336, 344
345, , 119025, 119369
346, , -119716, -347
347, , -120409, -120756
348, , 121104, 348
349, , 121801, 122149
350, , -122500, -351
351, , -123201, -123552
352, , 123904, 352
353, , 124609, 124961
354, , -125316, -355
355, , -126025, -126380
356, , 126736, 356
357, , 127449, 127805
358, , -128164, -359
359, , -128881, -129240
360, , 129600, 360
361, , 130321, 130681
362, , -131044, -363
363, , -131769, -132132
364, , 132496, 364
365, , 133225, 133589
366, , -133956, -367
367, , -134689, -135056
368, , 135424, 368
369, , 136161, 136529
370, , -136900, -371
371, , -137641, -138012
372, , 138384, 372
373, , 139129, 139501
374, , -139876, -375
375, , -140625, -141000
376, , 141376, 376
377, , 142129, 142505
378, , -142884, -379
379, , -143641, -144020
380, , 144400, 380
381, , 145161, 145541
382, , -145924, -383
383, , -146689, -147072
384, , 147456, 384
385, , 148225, 148609
386, , -148996, -387
387, , -149769, -150156
388, , 150544, 388
389, , 151321, 151709
390, , -152100, -391
391, , -152881, -153272
392, , 153664, 392
393, , 154449, 154841
394, , -155236, -395
395, , -156025, -156420
396, , 156816, 396
397, , 157609, 158005
398, , -158404, -399
399, , -159201, -159600
400, , 160000, 400

--------------------------------

May 18, 2011
Sequence Series
by: Staff

--------------------------------

footnote (1) - Part II

151, , -22801, -22952
152, , 23104, 152
153, , 23409, 23561
154, , -23716, -155
155, , -24025, -24180
156, , 24336, 156
157, , 24649, 24805
158, , -24964, -159
159, , -25281, -25440
160, , 25600, 160
161, , 25921, 26081
162, , -26244, -163
163, , -26569, -26732
164, , 26896, 164
165, , 27225, 27389
166, , -27556, -167
167, , -27889, -28056
168, , 28224, 168
169, , 28561, 28729
170, , -28900, -171
171, , -29241, -29412
172, , 29584, 172
173, , 29929, 30101
174, , -30276, -175
175, , -30625, -30800
176, , 30976, 176
177, , 31329, 31505
178, , -31684, -179
179, , -32041, -32220
180, , 32400, 180
181, , 32761, 32941
182, , -33124, -183
183, , -33489, -33672
184, , 33856, 184
185, , 34225, 34409
186, , -34596, -187
187, , -34969, -35156
188, , 35344, 188
189, , 35721, 35909
190, , -36100, -191
191, , -36481, -36672
192, , 36864, 192
193, , 37249, 37441
194, , -37636, -195
195, , -38025, -38220
196, , 38416, 196
197, , 38809, 39005
198, , -39204, -199
199, , -39601, -39800
200, , 40000, 200
201, , 40401, 40601
202, , -40804, -203
203, , -41209, -41412
204, , 41616, 204
205, , 42025, 42229
206, , -42436, -207
207, , -42849, -43056
208, , 43264, 208
209, , 43681, 43889
210, , -44100, -211
211, , -44521, -44732
212, , 44944, 212
213, , 45369, 45581
214, , -45796, -215
215, , -46225, -46440
216, , 46656, 216
217, , 47089, 47305
218, , -47524, -219
219, , -47961, -48180
220, , 48400, 220
221, , 48841, 49061
222, , -49284, -223
223, , -49729, -49952
224, , 50176, 224
225, , 50625, 50849
226, , -51076, -227
227, , -51529, -51756
228, , 51984, 228
229, , 52441, 52669
230, , -52900, -231
231, , -53361, -53592
232, , 53824, 232
233, , 54289, 54521
234, , -54756, -235
235, , -55225, -55460
236, , 55696, 236
237, , 56169, 56405
238, , -56644, -239
239, , -57121, -57360
240, , 57600, 240
241, , 58081, 58321
242, , -58564, -243
243, , -59049, -59292
244, , 59536, 244
245, , 60025, 60269
246, , -60516, -247
247, , -61009, -61256
248, , 61504, 248
249, , 62001, 62249
250, , -62500, -251
251, , -63001, -63252
252, , 63504, 252
253, , 64009, 64261
254, , -64516, -255
255, , -65025, -65280
256, , 65536, 256
257, , 66049, 66305
258, , -66564, -259
259, , -67081, -67340
260, , 67600, 260
261, , 68121, 68381
262, , -68644, -263
263, , -69169, -69432
264, , 69696, 264
265, , 70225, 70489
266, , -70756, -267
267, , -71289, -71556
268, , 71824, 268
269, , 72361, 72629
270, , -72900, -271
271, , -73441, -73712
272, , 73984, 272
273, , 74529, 74801
274, , -75076, -275
275, , -75625, -75900
276, , 76176, 276
277, , 76729, 77005
278, , -77284, -279
279, , -77841, -78120
280, , 78400, 280
--------------------------------

May 18, 2011
Sequence Series
by: Staff

--------------------------------

footnote (1) - Part I


n, , Series, Sum
, , ,
1, , 1, 1
2, , -4, -3
3, , -9, -12
4, , 16, 4
5, , 25, 29
6, , -36, -7
7, , -49, -56
8, , 64, 8
9, , 81, 89
10, , -100, -11
11, , -121, -132
12, , 144, 12
13, , 169, 181
14, , -196, -15
15, , -225, -240
16, , 256, 16
17, , 289, 305
18, , -324, -19
19, , -361, -380
20, , 400, 20
21, , 441, 461
22, , -484, -23
23, , -529, -552
24, , 576, 24
25, , 625, 649
26, , -676, -27
27, , -729, -756
28, , 784, 28
29, , 841, 869
30, , -900, -31
31, , -961, -992
32, , 1024, 32
33, , 1089, 1121
34, , -1156, -35
35, , -1225, -1260
36, , 1296, 36
37, , 1369, 1405
38, , -1444, -39
39, , -1521, -1560
40, , 1600, 40
41, , 1681, 1721
42, , -1764, -43
43, , -1849, -1892
44, , 1936, 44
45, , 2025, 2069
46, , -2116, -47
47, , -2209, -2256
48, , 2304, 48
49, , 2401, 2449
50, , -2500, -51
51, , -2601, -2652
52, , 2704, 52
53, , 2809, 2861
54, , -2916, -55
55, , -3025, -3080
56, , 3136, 56
57, , 3249, 3305
58, , -3364, -59
59, , -3481, -3540
60, , 3600, 60
61, , 3721, 3781
62, , -3844, -63
63, , -3969, -4032
64, , 4096, 64
65, , 4225, 4289
66, , -4356, -67
67, , -4489, -4556
68, , 4624, 68
69, , 4761, 4829
70, , -4900, -71
71, , -5041, -5112
72, , 5184, 72
73, , 5329, 5401
74, , -5476, -75
75, , -5625, -5700
76, , 5776, 76
77, , 5929, 6005
78, , -6084, -79
79, , -6241, -6320
80, , 6400, 80
81, , 6561, 6641
82, , -6724, -83
83, , -6889, -6972
84, , 7056, 84
85, , 7225, 7309
86, , -7396, -87
87, , -7569, -7656
88, , 7744, 88
89, , 7921, 8009
90, , -8100, -91
91, , -8281, -8372
92, , 8464, 92
93, , 8649, 8741
94, , -8836, -95
95, , -9025, -9120
96, , 9216, 96
97, , 9409, 9505
98, , -9604, -99
99, , -9801, -9900
100, , 10000, 100
101, , 10201, 10301
102, , -10404, -103
103, , -10609, -10712
104, , 10816, 104
105, , 11025, 11129
106, , -11236, -107
107, , -11449, -11556
108, , 11664, 108
109, , 11881, 11989
110, , -12100, -111
111, , -12321, -12432
112, , 12544, 112
113, , 12769, 12881
114, , -12996, -115
115, , -13225, -13340
116, , 13456, 116
117, , 13689, 13805
118, , -13924, -119
119, , -14161, -14280
120, , 14400, 120
121, , 14641, 14761
122, , -14884, -123
123, , -15129, -15252
124, , 15376, 124
125, , 15625, 15749
126, , -15876, -127
127, , -16129, -16256
128, , 16384, 128
129, , 16641, 16769
130, , -16900, -131
131, , -17161, -17292
132, , 17424, 132
133, , 17689, 17821
134, , -17956, -135
135, , -18225, -18360
136, , 18496, 136
137, , 18769, 18905
138, , -19044, -139
139, , -19321, -19460
140, , 19600, 140
141, , 19881, 20021
142, , -20164, -143
143, , -20449, -20592
144, , 20736, 144
145, , 21025, 21169
146, , -21316, -147
147, , -21609, -21756
148, , 21904, 148
149, , 22201, 22349
150, , -22500, -151
--------------------------------

May 18, 2011
Sequence Series
by: S

The question:

Marc first writes the perfect squares as a sequence

1,4,9,16,25,36,49,64,81,100...

After the number 1, he then alternates by making two terms negative followed by leaving two terms negative. Marc?s new sequence is:

1,-4,-9,16,25,-36,-49,64,81,-100...

What is the sum of the first 2011 terms in this new sequence?


The answer:

The sum of the first 2011 terms is: -4,046,132

I used Excel to compute this answer.

The calculations from the spreadsheet are included as footnote (1).



Thanks for writing.

Staff
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