A046658 -id:A046658 - cp's OEIS frontend

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

Wolfdieter Lang

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

Cf. A000108, A046658, A046714, A046748.

[n le 1 select 1 else 5*Self(n-1) - Catalan(n-1): n in [1..40]]; // G. C. Greubel, Jul 28 2024

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 *)

@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

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.

cp's OEIS Frontend

A046885 Row sums of triangle A046658.

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