A302018 Expansion of 1/(1 - x*(1 + theta_3(x))/2), where theta_3() is the Jacobi theta function.

1, 1, 2, 3, 5, 9, 15, 26, 44, 75, 129, 220, 377, 644, 1101, 1883, 3219, 5506, 9414, 16098, 27527, 47069, 80488, 137630, 235343, 402427, 688134, 1176685, 2012085, 3440591, 5883279, 10060183, 17202533, 29415676, 50299693, 86010564, 147074801, 251492331, 430042340, 735356089, 1257431006

Offset

0,3

Links

Table of n, a(n) for n=0..40.

N. J. A. Sloane, Transforms

Eric Weisstein's World of Mathematics, Jacobi Theta Functions

Index entries for sequences related to sums of squares

Formula

G.f.: 1/(1 - x*Sum_{k>=0} x^(k^2)).

a(0) = 1; a(n) = Sum_{k=1..n} A010052(k-1)*a(n-k).

Mathematica

nmax = 40; CoefficientList[Series[1/(1 - x (1 + EllipticTheta[3, 0, x])/2), {x, 0, nmax}], x]
nmax = 40; CoefficientList[Series[1/(1 - x Sum[x^k^2, {k, 0, nmax}]), {x, 0, nmax}], x]

Crossrefs

Antidiagonal sums of A045847.

Cf. A010052, A032803, A181649, A302019.

Sequence in context: A073031 A114138 A114140 * A096816 A220127 A286887

Adjacent sequences: A302015 A302016 A302017 * A302019 A302020 A302021

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 30 2018

Status

approved