A320191 Number of integer solutions to a^2 + 2*b^2 + 3*c^2 + 10*d^2 = n.

1, 2, 2, 6, 6, 4, 12, 4, 2, 14, 2, 12, 22, 16, 24, 24, 30, 12, 18, 36, 12, 40, 48, 16, 36, 42, 12, 26, 40, 28, 60, 60, 26, 32, 36, 28, 42, 48, 36, 60, 74, 40, 8, 52, 60, 52, 132, 40, 46, 114, 14, 72, 48, 36, 120, 96, 72, 60, 64, 60, 100, 124, 60, 68, 126, 52, 60, 124

Offset

0,2

Comments

a(n) > 0 for n >= 0.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Formula

G.f.: theta_3(q) * theta_3(q^2) * theta_3(q^3) * theta_3(q^10).

Mathematica

CoefficientList[Series[Product[EllipticTheta[3, 0, q^k], {k, 1, 3}]*EllipticTheta[3, 0, q^10], {q, 0, 80}], q] (* G. C. Greubel, Oct 29 2018 *)

Prog

(PARI) q='q+O('q^80); Vec(prod(k=1, 3, eta(q^(2*k))^5/(eta(q^k)* eta(q^(4*k)))^2 )*eta(q^(20))^5/(eta(q^10)* eta(q^(40)))^2 ) \\ G. C. Greubel, Oct 29 2018

Crossrefs

Cf. A320138, A320139, A320140, A033712, A320188, A320189, A320190.

Sequence in context: A060779 A324650 A029594 * A320190 A320189 A320188

Adjacent sequences: A320188 A320189 A320190 * A320192 A320193 A320194

Keyword

nonn

Author

Seiichi Manyama, Oct 07 2018

Status

approved