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 A346047 #7 Jul 03 2021 02:52:03
%S A346047 1,1,1,0,1,2,2,2,4,8,10,13,24,42,61,90,156,265,410,646,1093,1834,2948,
%T A346047 4789,8050,13475,22129,36570,61435,103039,171384,286156,481691,810502,
%U A346047 1359194,2284789,3856974,6512001,10982193,18550116,31406597,53194727,90082902
%N A346047 a(0) = a(1) = a(2) = 1; a(n) = Sum_{k=1..n-3} a(k) * a(n-k-3).
%F A346047 G.f. A(x) satisfies: A(x) = 1 + x + x^2 + x^3 * A(x) * (A(x) - 1).
%F A346047 a(n) ~ sqrt((3 - 3*r^3 - 4*r^4 - 2*r^5)/(8*Pi)) / (n^(3/2) * r^(n+3)), where r = 0.5701490701528437821032230160646366013461622472504286581627... is the root of the equation 1 - 2*r^3 - 4*r^4 - 4*r^5 + r^6 = 0. - _Vaclav Kotesovec_, Jul 03 2021
%t A346047 a[0] = a[1] = a[2] = 1; a[n_] := a[n] = Sum[a[k] a[n - k - 3], {k, 1, n - 3}]; Table[a[n], {n, 0, 42}]
%t A346047 nmax = 42; A[_] = 0; Do[A[x_] = 1 + x + x^2 + x^3 A[x] (A[x] - 1) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%Y A346047 Cf. A025250, A050253, A307970, A343304, A346048, A346049.
%K A346047 nonn
%O A346047 0,6
%A A346047 _Ilya Gutkovskiy_, Jul 02 2021