A343305 - OEIS

%I #4 Apr 11 2021 16:15:06

%S 1,1,1,1,1,2,3,4,5,7,11,17,25,36,53,81,125,191,289,439,675,1046,1621,

%T 2506,3877,6023,9395,14681,22947,35890,56231,88285,138825,218493,

%U 344145,542618,856597,1353766,2141383,3389797,5370219,8514773,13511673,21456808,34096503,54216636

%N a(0) = ... = a(3) = 1; a(n) = a(n-4) + Sum_{k=0..n-5} a(k) * a(n-k-5).

%F G.f. A(x) satisfies: A(x) = 1 + x + x^2 + x^3 + x^4 * A(x) + x^5 * A(x)^2.

%t a[0] = a[1] = a[2] = a[3] = 1; a[n_] := a[n] = a[n - 4] + Sum[a[k] a[n - k - 5], {k, 0, n - 5}]; Table[a[n], {n, 0, 45}]

%t nmax = 45; A[_] = 0; Do[A[x_] = 1 + x + x^2 + x^3 + x^4 A[x] + x^5 A[x]^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

%Y Cf. A001006, A050253, A307972, A343304.

%K nonn

%O 0,6

%A _Ilya Gutkovskiy_, Apr 11 2021