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Number of integer solutions to a^2 + 2*b^2 + 3*c^2 + 4*d^2 = n.
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%I #20 Oct 30 2018 05:41:50

%S 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,

%T 86,24,50,72,40,60,80,38,48,112,48,72,96,64,80,120,64,48,124,52,104,

%U 96,64,106,110,110,96,144,72,128,160,60,132,120,64,144,160,60,112,164

%N Number of integer solutions to a^2 + 2*b^2 + 3*c^2 + 4*d^2 = n.

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

%H Seiichi Manyama, <a href="/A320139/b320139.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^4).

%t CoefficientList[Series[Product[EllipticTheta[3, 0, q^k], {k, 1, 4}], {q, 0, 70}], q] (* _G. C. Greubel_, Oct 29 2018 *)

%o (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

%Y Cf. A320138, A320140, A033712, A320188, A320189, A320190, A320191.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Oct 06 2018