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%I #7 Jul 31 2021 09:44:21
%S 1,1,1,1,1,3,6,10,15,27,55,111,210,388,741,1473,2956,5856,11514,22806,
%T 45756,92394,186459,375867,759519,1541803,3140775,6407307,13081230,
%U 26745378,54797850,112495734,231270690,475960278,980643070,2023057266,4178837181,8641346835
%N G.f. A(x) satisfies: A(x) = 1 + x + x^2 + x^3 + x^4 * A(x)^3.
%F a(0) = ... = a(3) = 1; a(n) = Sum_{i=0..n-4} Sum_{j=0..n-i-4} a(i) * a(j) * a(n-i-j-4).
%t nmax = 37; A[_] = 0; Do[A[x_] = 1 + x + x^2 + x^3 + x^4 A[x]^3 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t a[n_] := a[n] = If[n < 4, 1, Sum[Sum[a[i] a[j] a[n - i - j - 4], {j, 0, n - i - 4}], {i, 0, n - 4}]]; Table[a[n], {n, 0, 37}]
%Y Cf. A001764, A019497, A307971, A346733, A346735.
%K nonn
%O 0,6
%A _Ilya Gutkovskiy_, Jul 30 2021