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A346051 G.f. A(x) satisfies: A(x) = 1 + x^2 + x^3 * A(x/(1 - x)) / (1 - x).

%I A346051 #12 Nov 30 2022 08:25:02
%S A346051 1,0,1,1,1,2,5,12,28,68,181,531,1671,5491,18627,65299,237880,903907,
%T A346051 3580619,14729777,62639952,274442521,1236730244,5729809348,
%U A346051 27292248240,133614280479,671803041553,3464970976743,18309428363425,99010800275743,547462187824465,3093329527120022
%N A346051 G.f. A(x) satisfies: A(x) = 1 + x^2 + x^3 * A(x/(1 - x)) / (1 - x).
%H A346051 G. C. Greubel, <a href="/A346051/b346051.txt">Table of n, a(n) for n = 0..695</a>
%F A346051 a(0) = 1, a(1) = 0, a(2) = 1; a(n) = Sum_{k=0..n-3} binomial(n-3,k) * a(k).
%t A346051 nmax = 31; A[_] = 0; Do[A[x_] = 1 + x^2 + x^3 A[x/(1 - x)]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t A346051 a[0] = 1; a[1] = 0; a[2] = 1; a[n_] := a[n] = Sum[Binomial[n - 3, k] a[k], {k, 0, n - 3}]; Table[a[n], {n, 0, 31}]
%o A346051 (Magma)
%o A346051 function a(n)
%o A346051   if n lt 3 then return (1+(-1)^n)/2;
%o A346051   else return (&+[Binomial(n-3,j)*a(j): j in [0..n-3]]);
%o A346051   end if; return a;
%o A346051 end function;
%o A346051 [a(n): n in [0..35]]; // _G. C. Greubel_, Nov 30 2022
%o A346051 (SageMath)
%o A346051 @CachedFunction
%o A346051 def a(n): # a = A346051
%o A346051     if (n<3): return (1, 0, 1)[n]
%o A346051     else: return sum(binomial(n-3, k)*a(k) for k in range(n-2))
%o A346051 [a(n) for n in range(51)] # _G. C. Greubel_, Nov 30 2022
%Y A346051 Cf. A000994, A000995, A000996, A000997, A000998.
%Y A346051 Cf. A007476, A210540, A346050, A346052.
%K A346051 nonn
%O A346051 0,6
%A A346051 _Ilya Gutkovskiy_, Jul 02 2021