A347802 Expansion of ( Sum_{k>=0} k^2 * q^(k^2) )^3.

0, 0, 0, 1, 0, 0, 12, 0, 0, 48, 0, 27, 64, 0, 216, 0, 0, 432, 48, 243, 0, 384, 972, 0, 768, 0, 864, 804, 0, 3456, 600, 0, 0, 1968, 3888, 1350, 3072, 0, 5508, 0, 0, 7776, 2400, 6075, 1728, 9600, 1944, 0, 4096, 7776, 21600, 2022, 0, 3456, 17424, 0, 13824, 21552, 0, 19521, 0, 31104, 15984, 0, 0, 21600, 34896, 11907

Offset: 0

Author

Seiichi Manyama, Sep 14 2021

Keywords

• nonn

Links

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

Crossrefs

Cf. A000408, A002102, A037215, A347801, A347803.

Programs

PARI

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

PARI

my(N=66, x='x+O('x^N)); concat([0, 0, 0], Vec(sum(k=0, sqrtint(N), k^2*x^k^2)^3))

Formula

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