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A123963 A triangular sequence from the omega(3) Jacobian Elliptic Modular equation. 0
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; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

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}

REFERENCES

Eric Weisstein's World of Mathematics, "Modular Equation." http://mathworld.wolfram.com/ModularEquation.html

LINKS

Table of n, a(n) for n=1..43.

FORMULA

t(n,m) =n^4 - m^4 + 2*n*m*(1 - n^2*m^2)

EXAMPLE

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}

MATHEMATICA

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]

CROSSREFS

Sequence in context: A286429 A280935 A067650 * A073396 A302553 A300132

Adjacent sequences:  A123960 A123961 A123962 * A123964 A123965 A123966

KEYWORD

uned,sign

AUTHOR

Roger L. Bagula, Oct 28 2006

STATUS

approved

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Last modified May 19 08:25 EDT 2019. Contains 323389 sequences. (Running on oeis4.)