A346077 a(n) = 1 + Sum_{k=1..n-5} a(k) * a(n-k-5).

1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 8, 12, 18, 26, 36, 49, 69, 101, 150, 221, 320, 460, 667, 981, 1456, 2161, 3191, 4698, 6932, 10283, 15324, 22870, 34103, 50813, 75770, 113229, 169590, 254340, 381579, 572537, 859511, 1291681, 1943489, 2926980, 4410709, 6649220, 10028570

Offset: 0

Author

Ilya Gutkovskiy, Jul 04 2021

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

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

Programs

Mathematica

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

SageMath

@CachedFunction
def a(n): # a = A346077
    if (n<6): return 1
    else: return 1 + sum(a(k)*a(n-k-5) for k in range(1,n-4))
[a(n) for n in range(51)] # G. C. Greubel, Nov 27 2022

Formula

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