A346075 a(n) = 1 + Sum_{k=1..n-3} a(k) * a(n-k-3).

1, 1, 1, 1, 2, 3, 4, 6, 10, 16, 25, 41, 69, 115, 192, 326, 558, 955, 1641, 2839, 4930, 8578, 14972, 26222, 46037, 80988, 142793, 252307, 446617, 791885, 1406394, 2501642, 4456080, 7947963, 14194221, 25379751, 45430710, 81409233, 146028788, 262192876, 471193406

Offset

0,5

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^3 * A(x) * (A(x) - 1).

Mathematica

a[n_] := a[n] = 1 + Sum[a[k] a[n - k - 3], {k, 1, n - 3}]; Table[a[n], {n, 0, 40}]
nmax = 40; A[_] = 0; Do[A[x_] = 1/(1 - x) + x^3 A[x] (A[x] - 1) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Prog

(SageMath)
@CachedFunction
def a(n): # a = A346075
    if (n<4): return 1
    else: return 1 + sum(a(k)*a(n-k-3) for k in range(1, n-2))
[a(n) for n in range(51)] # G. C. Greubel, Nov 27 2022

Crossrefs

Cf. A105633, A216604, A217282, A307970, A343304, A346047, A346076, A346077.

Sequence in context: A173697 A017986 A343304 * A352946 A342759 A293632

Adjacent sequences: A346072 A346073 A346074 * A346076 A346077 A346078

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 04 2021

Status

approved