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

Offset: 0

Author

N. J. A. Sloane, May 12 2010

Keywords

• nonn

Crossrefs

x^2+y^2+k*z^2: A005875, A014455, A034933, A169784.

Programs

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)];

Formula

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