A320139 Number of integer solutions to a^2 + 2*b^2 + 3*c^2 + 4*d^2 = n.

1, 2, 2, 6, 8, 8, 16, 16, 14, 22, 24, 16, 22, 32, 12, 32, 44, 16, 42, 52, 36, 40, 64, 32, 40, 86, 24, 50, 72, 40, 60, 80, 38, 48, 112, 48, 72, 96, 64, 80, 120, 64, 48, 124, 52, 104, 96, 64, 106, 110, 110, 96, 144, 72, 128, 160, 60, 132, 120, 64, 144, 160, 60, 112, 164

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^4).

Mathematica

CoefficientList[Series[Product[EllipticTheta[3, 0, q^k], {k, 1, 4}], {q, 0, 70}], q] (* G. C. Greubel, Oct 29 2018 *)

Prog

(PARI) q='q+O('q^70); Vec(prod(k=1, 4, eta(q^(2*k))^5/(eta(q^k)* eta(q^(4*k)))^2 )) \\ G. C. Greubel, Oct 29 2018

Crossrefs

Cf. A320138, A320140, A033712, A320188, A320189, A320190, A320191.

Sequence in context: A167878 A351928 A331786 * A033724 A033748 A033736

Adjacent sequences: A320136 A320137 A320138 * A320140 A320141 A320142

Keyword

nonn

Author

Seiichi Manyama, Oct 06 2018

Status

approved