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

0,8

Links

Table of n, a(n) for n=0..100.

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]

Prog

(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 */

Crossrefs

Cf. A156384

Sequence in context: A308046 A289323 A086937 * A291289 A095759 A260309

Adjacent sequences: A213021 A213022 A213023 * A213025 A213026 A213027

Keyword

nonn

Author

Max Alekseyev, Sep 29 2012

Status

approved