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 A346075 #10 Nov 28 2022 01:45:47
%S A346075 1,1,1,1,2,3,4,6,10,16,25,41,69,115,192,326,558,955,1641,2839,4930,
%T A346075 8578,14972,26222,46037,80988,142793,252307,446617,791885,1406394,
%U A346075 2501642,4456080,7947963,14194221,25379751,45430710,81409233,146028788,262192876,471193406
%N A346075 a(n) = 1 + Sum_{k=1..n-3} a(k) * a(n-k-3).
%H A346075 G. C. Greubel, <a href="/A346075/b346075.txt">Table of n, a(n) for n = 0..1000</a>
%F A346075 G.f. A(x) satisfies: A(x) = 1 / (1 - x) + x^3 * A(x) * (A(x) - 1).
%t A346075 a[n_] := a[n] = 1 + Sum[a[k] a[n - k - 3], {k, 1, n - 3}]; Table[a[n], {n, 0, 40}]
%t A346075 nmax = 40; A[_] = 0; Do[A[x_] = 1/(1 - x) + x^3 A[x] (A[x] - 1) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%o A346075 (SageMath)
%o A346075 @CachedFunction
%o A346075 def a(n): # a = A346075
%o A346075 if (n<4): return 1
%o A346075 else: return 1 + sum(a(k)*a(n-k-3) for k in range(1,n-2))
%o A346075 [a(n) for n in range(51)] # _G. C. Greubel_, Nov 27 2022
%Y A346075 Cf. A105633, A216604, A217282, A307970, A343304, A346047, A346076, A346077.
%K A346075 nonn
%O A346075 0,5
%A A346075 _Ilya Gutkovskiy_, Jul 04 2021