A303908 Expansion of 1/(2 + x - theta_2(sqrt(x))/(2*x^(1/8))), where theta_2() is the Jacobi theta function.
1, 0, 0, 1, 0, 0, 2, 0, 0, 3, 1, 0, 5, 2, 0, 9, 5, 0, 15, 10, 1, 27, 20, 3, 46, 40, 9, 80, 78, 22, 139, 152, 51, 242, 290, 114, 427, 550, 247, 753, 1034, 525, 1340, 1933, 1092, 2396, 3602, 2237, 4312, 6685, 4519, 7813, 12380, 9027, 14239, 22877, 17866, 26110, 42214, 35072, 48123, 77829, 68379
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..10000
- Eric Weisstein's World of Mathematics, Jacobi Theta Functions
- Index entries for sequences related to compositions
Programs
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Maple
a:= proc(n) option remember; `if`(n<0, 0, `if`(n=0, 1, add(a(n-j*(j+1)/2), j=2..isqrt(2*n)))) end: seq(a(n), n=0..80); # Alois P. Heinz, May 02 2018 -
Mathematica
nmax = 62; CoefficientList[Series[1/(2 + x - EllipticTheta[2, 0, Sqrt[x]]/(2 x^(1/8))), {x, 0, nmax}], x] nmax = 62; CoefficientList[Series[1/(1 - Sum[x^(k (k + 1)/2), {k, 2, nmax}]), {x, 0, nmax}], x] a[0] = 1; a[n_] := a[n] = Sum[SquaresR[1, 8 k + 1] a[n - k], {k, 2, n}]/2; Table[a[n], {n, 0, 62}]
Formula
G.f.: 1/(1 - Sum_{k>=2} x^(k*(k+1)/2)).
Comments