A167710 a(n) = 10*2^n - 3*A083658(n+2).

1, 5, 13, 35, 79, 185, 397, 875, 1831, 3905, 8053, 16835, 34399, 70985, 144157, 294875, 596311, 1212305, 2444293, 4947635, 9954319, 20085785, 40348717, 81228875, 162989191, 327572705, 656739733, 1318262435, 2641307839, 5296964585, 10608278077, 21259602875

Offset: 0

Author

Paul Curtz, Nov 10 2009

Keywords

• nonn
• easy

Comments

The sequence can be defined as the row sums of the triangle T(n,k)

.1;

.3,.2;

.3,.6,.4;

.9,.6,12,.8;

.9,18,12,24,16;

27,18,36,24,48,32;

with left column A162436, diagonal the powers of 2, and the recurrence T(n+2,k) = 3*T(n,k).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,3,-6).

Programs

Mathematica

LinearRecurrence[{2,3,-6},{1,5,13},40] (* Harvey P. Dale, Oct 03 2014 *)

Formula

a(n+1) - 2*a(n) = A162436(n+2).

a(n) = 2*a(n-1) + 3*a(n-2) - 6*a(n-3).

G.f.: (1+3*x)/((2*x-1) * (3*x^2-1)). - R. J. Mathar, Feb 27 2010

Extensions

Replaced cross-references by link to the index - R. J. Mathar, Feb 27 2010