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A320191
Number of integer solutions to a^2 + 2*b^2 + 3*c^2 + 10*d^2 = n.
8
1, 2, 2, 6, 6, 4, 12, 4, 2, 14, 2, 12, 22, 16, 24, 24, 30, 12, 18, 36, 12, 40, 48, 16, 36, 42, 12, 26, 40, 28, 60, 60, 26, 32, 36, 28, 42, 48, 36, 60, 74, 40, 8, 52, 60, 52, 132, 40, 46, 114, 14, 72, 48, 36, 120, 96, 72, 60, 64, 60, 100, 124, 60, 68, 126, 52, 60, 124
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^10).
MATHEMATICA
CoefficientList[Series[Product[EllipticTheta[3, 0, q^k], {k, 1, 3}]*EllipticTheta[3, 0, q^10], {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^(20))^5/(eta(q^10)* eta(q^(40)))^2 ) \\ G. C. Greubel, Oct 29 2018
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 07 2018
STATUS
approved