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%I #4 Aug 03 2018 08:18:39
%S 1,3,4,4,6,7,6,6,7,9,12,10,10,15,10,6,12,15,16,18,16,16,18,12,12,18,
%T 24,22,24,25,10,18,19,18,30,26,24,33,30,12,24,27,30,36,28,31,24,24,22,
%U 33,32,30,42,43,36,24,34,24,48,46,24,51,34,30,36,30,34,54,48,42,48,30,37,45,54,38
%N Expansion of (1 + theta_3(q))^3*(1 + theta_3(q^2))/16, where theta_3() is the Jacobi theta function.
%C Number of nonnegative integer solutions to the equation x^2 + y^2 + z^2 + 2*w^2 = n.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/JacobiThetaFunctions.html">Jacobi Theta Functions</a>
%e G.f. = 1 + 3*q + 4*q^2 + 4*q^3 + 6*q^4 + 7*q^5 + 6*q^6 + 6*q^7 + 7*q^8 + ...
%t nmax = 75; CoefficientList[Series[(1 + EllipticTheta[3, 0, q])^3 (1 + EllipticTheta[3, 0, q^2])/16, {q, 0, nmax}], q]
%t nmax = 75; CoefficientList[Series[(1 + QPochhammer[-q, -q]/QPochhammer[q, -q])^3 (1 + QPochhammer[-q^2, -q^2]/QPochhammer[q^2, -q^2])/16, {q, 0, nmax}], q]
%Y Cf. A014110, A156384, A236928.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Aug 02 2018
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