A213024 The number of solutions to x^2 + y^2 + 2*z^2 = n in positive integers x,y,z.

0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 1, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 6, 0, 0, 4, 0, 2, 4, 2, 3, 4, 2, 2, 2, 0, 6, 4, 2, 4, 0, 4, 2, 4, 2, 0, 8, 2, 2, 6, 0, 2, 8, 2, 6, 4, 0, 6, 1, 0, 4, 6, 4, 4, 6, 2, 2, 6, 2, 4, 8, 4, 0, 4, 2, 2, 10, 4, 6, 4, 2, 6, 2, 2, 8, 6, 6, 6, 0, 2, 0, 8, 6, 2, 9

Offset: 0

Author

Max Alekseyev, Sep 29 2012

Keywords

• nonn

Crossrefs

Cf. A156384

Programs

PARI

N=166; x='x+O('x^N);
T(x)=sum(k=1, 1+sqrtint(N), x^(k*k) );
gf=T(x)^2 * T(x^2);
v=Vec('a0 + gf );  v[1]=0;  v
/* Joerg Arndt, Oct 01 2012 */

Formula

a(n) = ( A014455(n) - 2*A033715(n) - A004018(n) + A000122(n/2) + 2*A000122(n) - A000007(n) )/8.

G.f.: T(x)^2 * T(x^2) where T(x) = sum(k>=1, x^(k^2)). [Joerg Arndt, Oct 01 2012]