A320189 Number of integer solutions to a^2 + 2*b^2 + 3*c^2 + 8*d^2 = n.

1, 2, 2, 6, 6, 4, 12, 4, 4, 18, 4, 20, 30, 12, 36, 24, 10, 32, 14, 24, 48, 32, 36, 40, 24, 18, 28, 34, 36, 60, 60, 28, 28, 40, 16, 56, 78, 44, 108, 68, 8, 72, 24, 40, 144, 60, 72, 112, 30, 46, 42, 64, 84, 116, 120, 40, 72, 84, 28, 116, 96, 60, 180, 68, 34, 120, 60, 64, 192, 80

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^8).

Mathematica

CoefficientList[Series[Product[EllipticTheta[3, 0, q^k], {k, 1, 3}]*EllipticTheta[3, 0, q^8], {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^(16))^5/(eta(q^8)* eta(q^(32)))^2 ) \\ G. C. Greubel, Oct 29 2018

Crossrefs

Cf. A320138, A320139, A320140, A033712, A320188, A320190, A320191.

Sequence in context: A029594 A320191 A320190 * A320188 A033712 A033730

Adjacent sequences: A320186 A320187 A320188 * A320190 A320191 A320192

Keyword

nonn

Author

Seiichi Manyama, Oct 07 2018

Status

approved