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%I #12 Oct 08 2018 06:52:43
%S 1,2,0,2,6,2,4,4,4,14,0,0,14,4,4,0,6,12,8,4,2,20,0,4,20,2,8,10,12,4,4,
%T 4,16,32,0,0,26,4,0,12,0,20,8,4,8,6,4,4,42,18,0,8,20,12,16,0,12,48,8,
%U 8,0,16,8,12,14,0,16,4,20,24,4,0,36,28,0,2,20,8,8,4,6
%N Expansion of theta_3(q) * theta_3(q^3) * theta_3(q^5), where theta_3() is the Jacobi theta function.
%C Also the number of integer solutions (a_1, a_2, a_3) to the equation a_1^2 + 3*a_2^2 + 5*a_3^2 = n.
%H Seiichi Manyama, <a href="/A320239/b320239.txt">Table of n, a(n) for n = 0..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/JacobiThetaFunctions.html">Jacobi Theta Functions</a>
%Y Product_{k=1..m} theta_3(q^(2*k-1)): A000122 (m=1), A033716 (m=2), this sequence (m=3), A320240 (m=4).
%Y Cf. A320078.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Oct 08 2018