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Search: id:A123963
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| A123963 |
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A triangular sequence from the omega(3) Jacobian Elliptic Modular equation. |
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+0
1
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| 0, -1, 0, -16, -27, -120, -81, -128, -485, -1440, -256, -375, -1248, -3607, -8160, -625, -864, -2589, -7264, -16329, -31200, -1296, -1715, -4712, -12843, -28640, -54611, -93240, -2401, -3072, -7845, -20800, -45993, -87456, -149197, -235200, -4096, -5103, -12240, -31615, -69312, -131391, -223888
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Normally these functions are taken as implicit polynomials in two variables set equal to zero. Row Sum: Table[Sum[t[n, m], {n, 0, m}], {m, 0, 10}] {0, -1, -163, -2134, -13646, -58871, -197057, -551964, -1354620, -3001917,-6133567}
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REFERENCES
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Eric Weisstein's World of Mathematics, "Modular Equation." http://mathworld.wolfram.com/ModularEquation.html
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FORMULA
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t(n,m) =n^4 - m^4 + 2*n*m*(1 - n^2*m^2)
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EXAMPLE
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Triangular sequence:
{0},
{-1, 0},
{-16, -27, -120},
{-81, -128, -485, -1440},
{-256, -375, -1248, -3607, -8160},
{-625, -864, -2589, -7264, -16329, -31200},
{-1296, -1715,-4712, -12843, -28640, -54611, -93240},
{-2401, -3072, -7845, -20800, -45993, -87456, -149197, -235200},
{-4096, -5103, -12240, -31615, -69312, -131391, -223888, -352815, -524160},
{-6561, -8000, -18173, -45792, -99545, -188096, -320085, -504128, -748817, -1062720},
{-10000, -11979, -25944, -63859, -137664, -259275, -440584, -693459, -1029744, -1461259, -1999800}
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MATHEMATICA
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t[n_, m_] = n^4 - m^4 + 2*n*m*(1 - n^2*m^2) a = Table[Table[t[n, m], {n, 0, m}], {m, 0, 10}] Flatten[a]
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CROSSREFS
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Sequence in context: A088247 A032610 A067650 this_sequence A073396 A101857 A104010
Adjacent sequences: A123960 A123961 A123962 this_sequence A123964 A123965 A123966
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KEYWORD
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uned,probation,sign
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Oct 28 2006
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