A351707 - OEIS

%I #5 Feb 18 2022 03:03:59

%S 1,1,1,1,1,3,7,15,31,65,147,373,1051,3157,9761,30573,96965,313999,

%T 1049719,3654303,13284783,50268837,196638987,789611161,3238765671,

%U 13540348965,57710600953,251163156089,1118308871001,5100825621147,23838465463447,114044805729151

%N G.f. A(x) satisfies: A(x) = 1 + x + x^2 + x^3 + x^4 * A(x/(1 - x)) / (1 - x)^2.

%F a(0) = ... = a(3) = 1; a(n) = Sum_{k=0..n-4} binomial(n-3,k+1) * a(k).

%t nmax = 31; A[_] = 0; Do[A[x_] = 1 + x + x^2 + x^3 + x^4 A[x/(1 - x)]/(1 - x)^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

%t a[n_] := a[n] = If[n < 4, 1, Sum[Binomial[n - 3, k + 1] a[k], {k, 0, n - 4}]]; Table[a[n], {n, 0, 31}]

%Y Cf. A040027, A210541, A351437, A351660.

%K nonn

%O 0,6

%A _Ilya Gutkovskiy_, Feb 16 2022