A169783 - OEIS

A169783

Number of solutions to a^2 + b^2 + 4*c^2 = n.

1, 4, 4, 0, 6, 16, 8, 0, 12, 20, 8, 0, 8, 16, 16, 0, 6, 32, 12, 0, 24, 32, 8, 0, 24, 20, 24, 0, 0, 48, 16, 0, 12, 32, 16, 0, 30, 16, 24, 0, 24, 64, 16, 0, 24, 48, 16, 0, 8, 36, 28, 0, 24, 48, 32, 0, 48, 32, 8, 0, 0, 48, 32, 0, 6, 64, 32, 0, 48, 64, 16, 0, 36, 32, 40, 0, 24, 64, 16, 0, 24, 68

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..81.

FORMULA

G.f.: theta_3(q)^2*theta_3(q^4), where theta_3() is the Jacobi theta function. - Ilya Gutkovskiy, Aug 01 2018

MAPLE

t0:=Array(0..10000, 0); M:=15;

for i from -M to M do for j from -M to M do for k from -M to M do

t1:=i^2+j^2+4*k^2; t0[t1]:=t0[t1]+1; od: od: od:

[seq(t0[i], i=0..100)];