A347801 Expansion of ( Sum_{k>=0} k^2 * q^(k^2) )^2.

0, 0, 1, 0, 0, 8, 0, 0, 16, 0, 18, 0, 0, 72, 0, 0, 0, 32, 81, 0, 128, 0, 0, 0, 0, 288, 50, 0, 0, 200, 0, 0, 256, 0, 450, 0, 0, 72, 0, 0, 288, 800, 0, 0, 0, 648, 0, 0, 0, 0, 723, 0, 1152, 392, 0, 0, 0, 0, 882, 0, 0, 1800, 0, 0, 0, 1696, 0, 0, 512, 0, 0, 0, 1296, 1152, 2450, 0, 0, 0, 0, 0, 2048, 0, 162, 0, 0, 4176, 0, 0, 0, 3200, 1458

Offset

0,6

Links

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

Formula

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

Prog

(PARI) a(n) = sum(i=1, n, sum(j=1, n, (i^2+j^2==n)*(i*j)^2));
(PARI) my(N=99, x='x+O('x^N)); concat([0, 0], Vec(sum(k=0, sqrtint(N), k^2*x^k^2)^2))

Crossrefs

Cf. A000404, A000925, A037214, A347802, A347803.

Sequence in context: A257397 A075448 A271407 * A028593 A369380 A037216

Adjacent sequences: A347798 A347799 A347800 * A347802 A347803 A347804

Keyword

nonn

Author

Seiichi Manyama, Sep 14 2021

Status

approved