A346049 a(0) = ... = a(4) = 1; a(n) = Sum_{k=1..n-5} a(k) * a(n-k-5).

1, 1, 1, 1, 1, 0, 1, 2, 3, 4, 4, 4, 6, 10, 16, 24, 30, 37, 50, 74, 116, 175, 245, 332, 456, 654, 981, 1471, 2146, 3056, 4320, 6203, 9119, 13540, 19986, 29134, 42113, 61047, 89398, 132021, 195272, 287547, 421235, 616418, 905161, 1335648, 1976407, 2922982, 4313230

Offset: 0

Author

Ilya Gutkovskiy, Jul 02 2021

Keywords

• nonn

Links

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

Crossrefs

Cf. A025250, A307972, A343305, A346047, A346048.

Programs

Mathematica

a[0] = a[1] = a[2] = a[3] = a[4] = 1; a[n_] := a[n] = Sum[a[k] a[n - k - 5], {k, 1, n - 5}]; Table[a[n], {n, 0, 48}]
nmax = 48; A[] = 0; Do[A[x] = 1 + x + x^2 + x^3 + x^4 + x^5 A[x] (A[x] - 1) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

SageMath

@CachedFunction
def a(n): # a = A346049
    if (n<5): return 1
    else: return 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 28 2022

Formula

G.f. A(x) satisfies: A(x) = 1 + x + x^2 + x^3 + x^4 + x^5 * A(x) * (A(x) - 1).