%I #15 Oct 30 2018 04:07:09
%S 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,
%T 12,26,40,28,60,60,26,32,36,28,42,48,36,60,74,40,8,52,60,52,132,40,46,
%U 114,14,72,48,36,120,96,72,60,64,60,100,124,60,68,126,52,60,124
%N Number of integer solutions to a^2 + 2*b^2 + 3*c^2 + 10*d^2 = n.
%C a(n) > 0 for n >= 0.
%H Seiichi Manyama, <a href="/A320191/b320191.txt">Table of n, a(n) for n = 0..10000</a>
%F G.f.: theta_3(q) * theta_3(q^2) * theta_3(q^3) * theta_3(q^10).
%t 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 *)
%o (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
%Y Cf. A320138, A320139, A320140, A033712, A320188, A320189, A320190.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Oct 07 2018