A302862 a(n) = [x^n] (1 + theta_3(x))^n/(2^n*(1 - x)), where theta_3() is the Jacobi theta function.

1, 2, 4, 8, 20, 57, 160, 422, 1076, 2780, 7449, 20462, 56348, 153909, 418268, 1139703, 3126068, 8618611, 23801146, 65708424, 181391905, 501296216, 1387834518, 3848187985, 10680579812, 29660831057, 82415406493, 229156296047, 637659848888, 1775648562970, 4947475298595

Offset

0,2

Comments

a(n) = number of nonnegative solutions to (x_1)^2 + (x_2)^2 + ... + (x_n)^2 <= n.

Links

Table of n, a(n) for n=0..30.

Eric Weisstein's World of Mathematics, Jacobi Theta Functions

Index entries for sequences related to sums of squares

Mathematica

Table[SeriesCoefficient[(1 + EllipticTheta[3, 0, x])^n/(2^n (1 - x)), {x, 0, n}], {n, 0, 30}]
Table[SeriesCoefficient[1/(1 - x) Sum[x^k^2, {k, 0, n}]^n, {x, 0, n}], {n, 0, 30}]

Crossrefs

Cf. A000606, A003059, A010052, A224212, A224213, A287617, A302860, A302863.

Sequence in context: A082279 A113180 A000116 * A344490 A006407 A100447

Adjacent sequences: A302859 A302860 A302861 * A302863 A302864 A302865

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 14 2018

Status

approved