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

Author

Ilya Gutkovskiy, Mar 30 2018

Keywords

• nonn

Links

• N. J. A. Sloane, Transforms
• Eric Weisstein's World of Mathematics, Jacobi Theta Functions
• Index entries for sequences related to sums of squares

Crossrefs

Antidiagonal sums of A045847.

Cf. A010052, A032803, A181649, A302019.

Programs

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]

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).