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 A349609 #11 Nov 24 2021 09:20:19
%S A349609 0,0,1,1,3,4,8,8,13,15,20,22,28,31,39,43,52,54,64,69,79,83,96,102,112,
%T A349609 121,135,140,154,162,179,185,203,212,228,238,255,265,281,296,316,326,
%U A349609 349,359,382,394,416,429,451,469,494,508,532,547,573,587
%N A349609 Number of solutions to x^2 + y^2 <= n^2, where x, y are positive odd integers.
%H A349609 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F A349609 a(n) = [x^(n^2)] theta_2(x^4)^2 / (4 * (1 - x)).
%F A349609 a(n) = Sum_{k=0..n^2} A290081(k).
%F A349609 a(n) = A053415(n) / 4.
%e A349609 a(4) = 3 since there are solutions (1,1), (3,1), (1,3).
%t A349609 Table[SeriesCoefficient[EllipticTheta[2, 0, x^4]^2/(4 (1 - x)), {x, 0, n^2}], {n, 0, 55}]
%Y A349609 Cf. A000328, A000603, A001182, A008442, A053415, A290081, A349610, A349611.
%K A349609 nonn
%O A349609 0,5
%A A349609 _Ilya Gutkovskiy_, Nov 23 2021