A346077 - OEIS

%I #9 Nov 28 2022 01:45:41

%S 1,1,1,1,1,1,2,3,4,5,6,8,12,18,26,36,49,69,101,150,221,320,460,667,

%T 981,1456,2161,3191,4698,6932,10283,15324,22870,34103,50813,75770,

%U 113229,169590,254340,381579,572537,859511,1291681,1943489,2926980,4410709,6649220,10028570

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

%H G. C. Greubel, <a href="/A346077/b346077.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f. A(x) satisfies: A(x) = 1 / (1 - x) + x^5 * A(x) * (A(x) - 1).

%t a[n_] := a[n] = 1 + Sum[a[k] a[n - k - 5], {k, 1, n - 5}]; Table[a[n], {n, 0, 47}]

%t nmax = 47; A[_] = 0; Do[A[x_] = 1/(1 - x) + x^5 A[x] (A[x] - 1) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

%o (SageMath)

%o @CachedFunction

%o def a(n): # a = A346077

%o     if (n<6): return 1

%o     else: return 1 + sum(a(k)*a(n-k-5) for k in range(1,n-4))

%o [a(n) for n in range(51)] # _G. C. Greubel_, Nov 27 2022

%Y Cf. A105633, A217282, A307972, A346049, A346074, A346075, A346076.

%K nonn

%O 0,7

%A _Ilya Gutkovskiy_, Jul 04 2021