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Number of integer solutions to a^2 + 2*b^2 + 3*c^2 + 7*d^2 = n.
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%I #17 Oct 30 2018 03:35:58

%S 1,2,2,6,6,4,12,6,6,18,12,20,26,28,20,20,34,4,30,44,20,48,44,20,20,38,

%T 16,42,62,40,56,48,34,24,72,40,70,112,36,56,68,44,40,124,60,60,124,24,

%U 66,62,54,96,92,80,64,80,64,88,136,64,76,140,52,70,166,44,104,196,44

%N Number of integer solutions to a^2 + 2*b^2 + 3*c^2 + 7*d^2 = n.

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

%H Seiichi Manyama, <a href="/A320188/b320188.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^7).

%t CoefficientList[Series[Product[EllipticTheta[3, 0, q^k], {k, 1, 3}]*EllipticTheta[3,0,q^7], {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^(14))^5/(eta(q^7)* eta(q^(28)))^2 ) \\ _G. C. Greubel_, Oct 29 2018

%Y Cf. A320138, A320139, A320140, A033712, A320189, A320190, A320191.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Oct 07 2018