This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A317646 #5 Feb 16 2025 08:33:56
%S A317646 1,2,3,4,5,4,5,4,5,8,8,8,11,8,6,8,5,10,14,12,16,12,11,8,11,14,14,20,
%T A317646 18,12,14,12,5,20,19,20,30,16,17,16,16,18,24,20,25,28,14,16,11,22,25,
%U A317646 28,34,20,30,24,18,28,26,28,42,24,20,32,5,28,36,28,41,32,32,20,30,30,28,44
%N A317646 Expansion of (1 + theta_3(q))^2*(1 + theta_3(q^2))^2/16, where theta_3() is the Jacobi theta function.
%C A317646 Number of nonnegative integer solutions to the equation x^2 + y^2 + 2*z^2 + 2*w^2 = n.
%H A317646 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/JacobiThetaFunctions.html">Jacobi Theta Functions</a>
%e A317646 G.f. = 1 + 2*q + 3*q^2 + 4*q^3 + 5*q^4 + 4*q^5 + 5*q^6 + 4*q^7 + 5*q^8 + ...
%t A317646 nmax = 75; CoefficientList[Series[(1 + EllipticTheta[3, 0, q])^2 (1 + EllipticTheta[3, 0, q^2])^2/16, {q, 0, nmax}], q]
%t A317646 nmax = 75; CoefficientList[Series[(1 + QPochhammer[-q, -q]/QPochhammer[q, -q])^2 (1 + QPochhammer[-q^2, -q^2]/QPochhammer[q^2, -q^2])^2/16, {q, 0, nmax}], q]
%Y A317646 Cf. A014110, A097057, A317645.
%K A317646 nonn
%O A317646 0,2
%A A317646 _Ilya Gutkovskiy_, Aug 02 2018