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 A357308 #5 Sep 24 2022 14:59:47
%S A357308 0,0,1,1,1,1,1,2,4,7,11,16,24,39,67,116,196,324,534,892,1516,2601,
%T A357308 4463,7630,13022,22276,38286,66084,114328,197929,342783,594218,
%U A357308 1031794,1794944,3127450,5455272,9523812,16640542,29102938,50951070,89289998,156616648,274923328,482945930,848972814
%N A357308 a(0) = a(1) = 0, a(2) = 1; a(n) = a(n-1) + Sum_{k=0..n-3} a(k) * a(n-k-3).
%F A357308 G.f. A(x) satisfies: A(x) = x^2 * (1 + x * A(x)^2) / (1 - x).
%t A357308 a[0] = a[1] = 0; a[2] = 1; a[n_] := a[n] = a[n - 1] + Sum[a[k] a[n - k - 3], {k, 0, n - 3}]; Table[a[n], {n, 0, 44}]
%t A357308 nmax = 44; A[_] = 0; Do[A[x_] = x^2 (1 + x A[x]^2)/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%Y A357308 Cf. A006318, A023426, A023431, A025246, A346503, A346504, A357307.
%K A357308 nonn
%O A357308 0,8
%A A357308 _Ilya Gutkovskiy_, Sep 23 2022