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 A302862 #7 Feb 16 2025 08:33:53
%S A302862 1,2,4,8,20,57,160,422,1076,2780,7449,20462,56348,153909,418268,
%T A302862 1139703,3126068,8618611,23801146,65708424,181391905,501296216,
%U A302862 1387834518,3848187985,10680579812,29660831057,82415406493,229156296047,637659848888,1775648562970,4947475298595
%N A302862 a(n) = [x^n] (1 + theta_3(x))^n/(2^n*(1 - x)), where theta_3() is the Jacobi theta function.
%C A302862 a(n) = number of nonnegative solutions to (x_1)^2 + (x_2)^2 + ... + (x_n)^2 <= n.
%H A302862 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/JacobiThetaFunctions.html">Jacobi Theta Functions</a>
%H A302862 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%t A302862 Table[SeriesCoefficient[(1 + EllipticTheta[3, 0, x])^n/(2^n (1 - x)), {x, 0, n}], {n, 0, 30}]
%t A302862 Table[SeriesCoefficient[1/(1 - x) Sum[x^k^2, {k, 0, n}]^n, {x, 0, n}], {n, 0, 30}]
%Y A302862 Cf. A000606, A003059, A010052, A224212, A224213, A287617, A302860, A302863.
%K A302862 nonn
%O A302862 0,2
%A A302862 _Ilya Gutkovskiy_, Apr 14 2018