A080918 Number of integer solutions to the equation 2x^2+y^2+32z^2=n.

1, 2, 2, 4, 2, 0, 4, 0, 2, 6, 0, 4, 4, 0, 0, 0, 2, 4, 6, 4, 0, 0, 4, 0, 4, 2, 0, 8, 0, 0, 0, 0, 4, 12, 8, 8, 10, 0, 12, 0, 4, 16, 0, 12, 12, 0, 0, 0, 8, 10, 14, 16, 0, 0, 16, 0, 8, 12, 0, 20, 0, 0, 0, 0, 6, 16, 16, 4, 16, 0, 8, 0, 6, 12, 0, 12, 12, 0, 0, 0, 8, 14, 8, 20, 0, 0, 20, 0, 4, 20, 0, 8, 0

Offset: 0

Author

Michael Somos, Feb 23 2003

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• J. B. Tunnell, A classical Diophantine problem and modular forms of weight 3/2, Invent. Math., 72 (1983), 323-334.

Crossrefs

a(2n-1)=A072069(n).

Cf. A000122 (theta_3(q)), A080917.

Programs

PARI

{a(n)=my(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)^3*eta(x^4+A)^3*eta(x^64+A)^5/ (eta(x+A)*eta(x^8+A)*eta(x^32+A)*eta(x^128+A))^2, n))}

Formula

G.f.: theta_3(q) * theta_3(q^2) * theta_3(q^32).