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%I #7 Jul 03 2021 04:56:44
%S 1,1,1,1,0,1,2,3,3,3,5,9,15,19,24,35,59,95,137,191,280,445,706,1071,
%T 1575,2357,3663,5755,8890,13483,20518,31759,49658,77267,119135,183523,
%U 284793,444883,694798,1080865,1679142,2616399,4092497,6408249,10021176,15657643
%N a(0) = ... = a(3) = 1; a(n) = Sum_{k=1..n-4} a(k) * a(n-k-4).
%F G.f. A(x) satisfies: A(x) = 1 + x + x^2 + x^3 + x^4 * A(x) * (A(x) - 1).
%p a:= proc(n) option remember; `if`(n<4, 1,
%p add(a(j)*a(n-4-j), j=1..n-4))
%p end:
%p seq(a(n), n=0..45); # _Alois P. Heinz_, Jul 03 2021
%t a[0] = a[1] = a[2] = a[3] = 1; a[n_] := a[n] = Sum[a[k] a[n - k - 4], {k, 1, n - 4}]; Table[a[n], {n, 0, 45}]
%t nmax = 45; A[_] = 0; Do[A[x_] = 1 + x + x^2 + x^3 + x^4 A[x] (A[x] - 1) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%Y Cf. A025250, A307971, A343304, A343305, A346047, A346049.
%K nonn
%O 0,7
%A _Ilya Gutkovskiy_, Jul 02 2021
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