A374535 Expansion of (x/(8 * (1-x))) * d/dx(theta_3(x)^4).

0, 1, 7, 19, 31, 61, 133, 189, 213, 330, 510, 642, 786, 968, 1304, 1664, 1712, 2018, 2720, 3100, 3460, 4132, 4924, 5476, 5764, 6539, 7631, 8711, 9383, 10253, 12413, 13405, 13501, 15085, 16921, 18601, 20005, 21411, 23691, 25875, 26595, 28317, 32349, 34241, 35825, 39335, 42647, 44903

Offset: 0

Author

Seiichi Manyama, Jul 11 2024

Keywords

• nonn

Crossrefs

Partial sums of A185152.

Cf. A014203, A374534.

Programs

PARI

my(N=50, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, k^2*x^k/(1+(-x)^k)^2)/(1-x)))

Formula

a(n) = 1/8 * Sum_{i,j,k,l in Z and i^2 + j^2 + k^2 + l^2 <= n} i^2 + j^2 + k^2 + l^2.

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