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 A317642 #5 Feb 16 2025 08:33:56
%S A317642 1,0,2,0,0,2,0,4,2,0,0,0,0,4,0,0,0,0,2,0,2,0,4,4,0,0,0,0,4,0,0,0,2,0,
%T A317642 0,0,0,4,4,0,0,0,0,0,0,2,0,4,0,0,2,0,4,4,0,4,0,0,0,0,0,0,0,4,0,0,0,0,
%U A317642 0,0,4,0,2,0,0,0,0,8,0,0,2,0,4,0,0,0,0,0,4,0,0,0,4,0,0,4,0,0,6
%N A317642 Expansion of theta_3(q^2)*theta_3(q^5), where theta_3() is the Jacobi theta function.
%C A317642 Number of integer solutions to the equation 2*x^2 + 5*y^2 = n.
%H A317642 N. J. A. Sloane et al., <a href="https://oeis.org/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a> (Index to related sequences, programs, references)
%H A317642 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/JacobiThetaFunctions.html">Jacobi Theta Functions</a>
%F A317642 G.f.: Product_{k>=1} (1 + x^(4*k-2))^2*(1 - x^(4*k))*(1 + x^(10*k-5))^2*(1 - x^(10*k)).
%e A317642 G.f. = 1 + 2*q^2 + 2*q^5 + 4*q^7 + 2*q^8 + 4*q^13 + 2*q^18 + 2*q^20 + 4*q^22 + ...
%t A317642 nmax = 98; CoefficientList[Series[EllipticTheta[3, 0, q^2] EllipticTheta[3, 0, q^5], {q, 0, nmax}], q]
%t A317642 nmax = 98; CoefficientList[Series[QPochhammer[-q^2, -q^2] QPochhammer[-q^5, -q^5]/(QPochhammer[q^2, -q^2] QPochhammer[q^5, -q^5]), {q, 0, nmax}], q]
%Y A317642 Cf. A000286, A020674, A033718, A106889, A108563, A192323.
%K A317642 nonn
%O A317642 0,3
%A A317642 _Ilya Gutkovskiy_, Aug 02 2018