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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. 0
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

Table of n, a(n) for n=0..62.

Eric Weisstein's World of Mathematics, Jacobi Theta Functions

Index entries for sequences related to compositions

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

Cf. A000217, A023361, A212804, A280542, A303668, A303906, A303907.

Sequence in context: A029301 A263414 A162934 * A082660 A134673 A131636

Adjacent sequences:  A303905 A303906 A303907 * A303909 A303910 A303911

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, May 02 2018

STATUS

approved

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Last modified May 31 02:51 EDT 2020. Contains 334747 sequences. (Running on oeis4.)