login
A320139
Number of integer solutions to a^2 + 2*b^2 + 3*c^2 + 4*d^2 = n.
18
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
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
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 06 2018
STATUS
approved