A346050 - OEIS

%I #10 Nov 28 2022 02:05:25

%S 0,1,1,0,1,3,6,11,23,60,179,553,1716,5415,17801,61956,228391,882309,

%T 3530322,14531621,61454091,267479778,1200680113,5561767211,

%U 26553471186,130366882251,656668581417,3387887246292,17886582294921,96603394562849,533645344137390,3014295344076655

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

%H G. C. Greubel, <a href="/A346050/b346050.txt">Table of n, a(n) for n = 0..695</a>

%F a(0) = 0, a(1) = a(2) = 1; a(n) = Sum_{k=0..n-3} binomial(n-3,k) * a(k).

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

%t a[0] = 0; a[1] = 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 (SageMath)

%o @CachedFunction

%o def a(n): # a = A346050

%o     if (n<3): return (0,1,1)[n]

%o     else: return sum(binomial(n-3,k)*a(k) for k in range(n-2))

%o [a(n) for n in range(51)] # _G. C. Greubel_, Nov 28 2022

%Y Cf. A000994, A000995, A000996, A000997, A000998, A007476, A210540, A346051, A346052.

%K nonn

%O 0,6

%A _Ilya Gutkovskiy_, Jul 02 2021