A046885 Row sums of triangle A046658.

1, 4, 18, 85, 411, 2013, 9933, 49236, 244750, 1218888, 6077644, 30329434, 151439158, 756452890, 3779590010, 18888255205, 94405918355, 471899946985, 2359022096225, 11793343217935, 58960151969255, 294776293579255

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

a(n) = 2*5^(n-1) - A046714(n-1) = (A046748(n) - 5^(n-1))/2.

G.f.: x*(2 - c(x))/(1-5*x), where c(x) is the g.f. of A000108 (Catalan numbers).

Inhomogeneous recursion: a(n) = 5*a(n-1) - C(n-1), n >= 2, a(1)=1; C(n) = A000108(n) (Catalan).

Homogeneous recursion: a(n) = (3*(3*n-2)/n)*a(n-1) - (10*(2*n-3)/n)*a(n-2), n >= 3, a(1)=1, a(2)=4.

Mathematica

Rest@CoefficientList[Series[Sqrt[1-4*x]*(1-Sqrt[1-4*x])/(2*(1-5*x)), {x, 0, 40}], x] (* G. C. Greubel, Jul 28 2024 *)

Prog

(Magma)
[n le 1 select 1 else 5*Self(n-1) - Catalan(n-1): n in [1..40]]; // G. C. Greubel, Jul 28 2024
(SageMath)
@CachedFunction
def A046885(n): return 1 if n==1 else 5*A046885(n-1) - catalan_number(n-1)
[A046885(n) for n in range(1, 41)] # G. C. Greubel, Jul 28 2024

Crossrefs

Cf. A000108, A046658, A046714, A046748.

Sequence in context: A185132 A085923 A110166 * A247637 A055834 A079567

Adjacent sequences: A046882 A046883 A046884 * A046886 A046887 A046888

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved