Voozh

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

(list; graph; refs; listen; history; text; internal format)

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) );