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A303908 Expansion of 1/(2 + x - theta_2(sqrt(x))/(2*x^(1/8))), where theta_2() is the Jacobi theta function. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,7
COMMENTS
Number of compositions (ordered partitions) of n into triangular numbers > 1.
LINKS
Eric Weisstein's World of Mathematics, Jacobi Theta Functions
FORMULA
G.f.: 1/(1 - Sum_{k>=2} x^(k*(k+1)/2)).
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}]
CROSSREFS
Sequence in context: A029301 A263414 A162934 * A351592 A082660 A134673
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 02 2018
STATUS
approved

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)