A320190 Number of integer solutions to a^2 + 2*b^2 + 3*c^2 + 9*d^2 = n.

1, 2, 2, 6, 6, 4, 12, 4, 2, 16, 4, 12, 30, 16, 20, 40, 14, 8, 42, 8, 28, 60, 20, 32, 44, 22, 8, 46, 28, 36, 84, 36, 18, 40, 32, 8, 80, 40, 40, 120, 36, 24, 56, 40, 44, 140, 48, 48, 126, 22, 62, 64, 40, 68, 132, 72, 52, 120, 52, 60, 136, 56, 36, 160, 46, 64, 180, 40, 48

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^9).

Mathematica

CoefficientList[Series[Product[EllipticTheta[3, 0, q^k], {k, 1, 3}]*EllipticTheta[3, 0, q^9], {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^(18))^5/(eta(q^9)* eta(q^(36)))^2 ) \\ G. C. Greubel, Oct 29 2018

Crossrefs

Cf. A320138, A320139, A320140, A033712, A320188, A320189, A320191.

Sequence in context: A324650 A029594 A320191 * A320189 A320188 A033712

Adjacent sequences: A320187 A320188 A320189 * A320191 A320192 A320193

Keyword

nonn

Author

Seiichi Manyama, Oct 07 2018

Status

approved