A320188 Number of integer solutions to a^2 + 2*b^2 + 3*c^2 + 7*d^2 = n.

1, 2, 2, 6, 6, 4, 12, 6, 6, 18, 12, 20, 26, 28, 20, 20, 34, 4, 30, 44, 20, 48, 44, 20, 20, 38, 16, 42, 62, 40, 56, 48, 34, 24, 72, 40, 70, 112, 36, 56, 68, 44, 40, 124, 60, 60, 124, 24, 66, 62, 54, 96, 92, 80, 64, 80, 64, 88, 136, 64, 76, 140, 52, 70, 166, 44, 104, 196, 44

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^7).

Mathematica

CoefficientList[Series[Product[EllipticTheta[3, 0, q^k], {k, 1, 3}]*EllipticTheta[3, 0, q^7], {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^(14))^5/(eta(q^7)* eta(q^(28)))^2 ) \\ G. C. Greubel, Oct 29 2018

Crossrefs

Cf. A320138, A320139, A320140, A033712, A320189, A320190, A320191.

Sequence in context: A320191 A320190 A320189 * A033712 A033730 A033754

Adjacent sequences: A320185 A320186 A320187 * A320189 A320190 A320191

Keyword

nonn

Author

Seiichi Manyama, Oct 07 2018

Status

approved