A082413 a(n) = (2*9^n + 3^n)/3.

1, 7, 57, 495, 4401, 39447, 354537, 3189375, 28700001, 258286887, 2324542617, 20920765455, 188286534801, 1694577750327, 15251196564297, 137260759512735, 1235346806916801, 11118121176157767, 100063090327139577, 900567812169415215

Offset: 0

Author

Paul Barry, Apr 23 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A082412.

Links

• Nathaniel Johnston, Table of n, a(n) for n = 0..250
• Index entries for linear recurrences with constant coefficients, signature (12,-27).

Crossrefs

Cf. A082412, A082414.

Programs

Maple

seq((2*9^n+3^n)/3,n=0..19); # Nathaniel Johnston, Jun 26 2011

Formula

G.f.: (1-5*x)/((1-3*x)*(1-9*x));

E.g.f.: (2*exp(9*x) + exp(3*x))/3.

a(n) = (2*9^n + 3^n)/3.