login
Number of integer solutions to a^2 + 2*b^2 + 3*c^2 + 9*d^2 = n.
8

%I #15 Oct 30 2018 03:36:15

%S 1,2,2,6,6,4,12,4,2,16,4,12,30,16,20,40,14,8,42,8,28,60,20,32,44,22,8,

%T 46,28,36,84,36,18,40,32,8,80,40,40,120,36,24,56,40,44,140,48,48,126,

%U 22,62,64,40,68,132,72,52,120,52,60,136,56,36,160,46,64,180,40,48

%N Number of integer solutions to a^2 + 2*b^2 + 3*c^2 + 9*d^2 = n.

%C a(n) > 0 for n >= 0.

%H Seiichi Manyama, <a href="/A320190/b320190.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^9).

%t CoefficientList[Series[Product[EllipticTheta[3, 0, q^k], {k, 1, 3}]*EllipticTheta[3,0,q^9], {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^(18))^5/(eta(q^9)* eta(q^(36)))^2 ) \\ _G. C. Greubel_, Oct 29 2018

%Y Cf. A320138, A320139, A320140, A033712, A320188, A320189, A320191.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Oct 07 2018