A346076 a(n) = 1 + Sum_{k=1..n-4} a(k) * a(n-k-4).

1, 1, 1, 1, 1, 2, 3, 4, 5, 7, 11, 17, 25, 36, 54, 84, 131, 201, 307, 475, 745, 1172, 1837, 2878, 4531, 7173, 11381, 18057, 28669, 45624, 72796, 116336, 186066, 297865, 477505, 766621, 1232214, 1982292, 3191693, 5143974, 8298640, 13399691, 21652705, 35014373, 56663700

Offset

0,6

Links

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

Formula

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

Mathematica

a[n_] := a[n] = 1 + Sum[a[k] a[n - k - 4], {k, 1, n - 4}]; Table[a[n], {n, 0, 44}]
nmax = 44; A[_] = 0; Do[A[x_] = 1/(1 - x) + x^4 A[x] (A[x] - 1) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Prog

(SageMath)
@CachedFunction
def a(n): # a = A346076
    if (n<5): return 1
    else: return 1 + sum(a(k)*a(n-k-4) for k in range(1, n-3))
[a(n) for n in range(51)] # G. C. Greubel, Nov 27 2022

Crossrefs

Cf. A105633, A217282, A307971, A343305, A346048, A346073, A346075, A346077.

Sequence in context: A245823 A143284 A343305 * A339357 A279065 A327325

Adjacent sequences: A346073 A346074 A346075 * A346077 A346078 A346079

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 04 2021

Status

approved