A347803 Expansion of ( Sum_{k>=0} k^2 * q^(k^2) )^4.

0, 0, 0, 0, 1, 0, 0, 16, 0, 0, 96, 0, 36, 256, 0, 432, 256, 0, 1728, 64, 486, 2304, 768, 3888, 0, 3072, 7776, 1728, 7112, 0, 13824, 12864, 0, 27648, 6336, 15552, 9261, 18688, 62208, 21744, 24576, 0, 72576, 51456, 24300, 117504, 38400, 101088, 9216, 93184, 155520, 86400, 142382, 62208, 352512, 67344, 0, 202752, 286176

Offset: 0

Author

Seiichi Manyama, Sep 14 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000414, A014110, A037216, A347801, A347802.

Programs

PARI

a(n) = sum(i=1, n, sum(j=1, n, sum(k=1, n, sum(m=1, n, (i^2+j^2+k^2+m^2==n)*(i*j*k*m)^2))));

PARI

my(N=66, x='x+O('x^N)); concat([0, 0, 0, 0], Vec(sum(k=0, sqrtint(N), k^2*x^k^2)^4))

Formula

a(n) is sum of i^2 * j^2 * k^2 *m^2 for positive integers i,j,k,m such that i^2+j^2+k^2+m^2=n.