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 A349611 #14 Dec 21 2023 15:47:09
%S A349611 0,0,1,1,5,11,32,44,82,120,207,277,405,541,768,966,1272,1592,2087,
%T A349611 2489,3103,3719,4588,5348,6386,7522,8891,10175,11909,13623,15818,
%U A349611 17742,20278,22720,25923,28917,32361,36031,40368,44488,49400,54358,60377,65835,72341
%N A349611 Number of solutions to x^2 + y^2 + z^2 + w^2 <= n^2, where x, y, z, w are positive odd integers.
%H A349611 Robert Israel, <a href="/A349611/b349611.txt">Table of n, a(n) for n = 0..2500</a>
%H A349611 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F A349611 a(n) = [x^(n^2)] theta_2(x^4)^4 / (16 * (1 - x)).
%e A349611 a(4) = 5 since there are solutions (1,1,1,1), (3,1,1,1), (1,3,1,1), (1,1,3,1), (1,1,1,3).
%p A349611 N:= 100: # for a(0) .. a(N)
%p A349611 F:= add(x^(k^2),k = 1 ... N,2):
%p A349611 F:= expand(F^4):
%p A349611 L:= ListTools:-PartialSums([seq](coeff(F,x,n),n=0..N^2)):
%p A349611 L[[seq(n^2+1,n=0..N)]]; # _Robert Israel_, Dec 21 2023
%t A349611 Table[SeriesCoefficient[EllipticTheta[2, 0, x^4]^4/(16 (1 - x)), {x, 0, n^2}], {n, 0, 44}]
%Y A349611 Cf. A055403, A055410, A341423, A349609, A349610.
%K A349611 nonn
%O A349611 0,5
%A A349611 _Ilya Gutkovskiy_, Nov 23 2021