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 A304633 #5 Feb 16 2025 08:33:54
%S A304633 1,1,1,1,2,2,2,2,3,4,4,4,5,7,7,7,9,12,13,13,16,20,23,23,27,35,41,42,
%T A304633 47,61,71,75,82,104,124,134,146,178,217,237,258,307,377,419,456,535,
%U A304633 651,739,804,933,1126,1300,1422,1629,1955,2275,2513,2846,3397,3972,4435,4990,5904
%N A304633 Expansion of 2/((1 - x)*(3 + 2*x - theta_3(x))), where theta_3() is the Jacobi theta function.
%C A304633 Partial sums of A280542.
%H A304633 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/JacobiThetaFunctions.html">Jacobi Theta Functions</a>
%H A304633 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%H A304633 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F A304633 G.f.: 1/((1 - x)*(1 - Sum_{k>=2} x^(k^2))).
%t A304633 nmax = 62; CoefficientList[Series[2/((1 - x) (3 + 2 x - EllipticTheta[3, 0, x])), {x, 0, nmax}], x]
%t A304633 nmax = 62; CoefficientList[Series[1/((1 - x) (1 - Sum[x^k^2, {k, 2, nmax}])), {x, 0, nmax}], x]
%t A304633 a[0] = 1; a[n_] := a[n] = Sum[Boole[IntegerQ[k^(1/2)] && k != 1] a[n - k], {k, 1, n}]; Accumulate[Table[a[n], {n, 0, 62}]]
%Y A304633 Cf. A000290, A001156, A006456, A010052, A248801, A280542, A302833, A303667.
%K A304633 nonn
%O A304633 0,5
%A A304633 _Ilya Gutkovskiy_, May 15 2018