A165149 a(n) = (3*9^n - 5^n)/2.

1, 11, 109, 1031, 9529, 87011, 789349, 7135391, 64374769, 580154171, 5225293789, 47047175351, 423522234409, 3812188390931, 34312136924629, 308821439352911, 2779453989332449, 25015391079773291, 225140045596865869, 2026268039766324071, 18236450504869572889, 164128245278689437251

Offset: 0

Author

Klaus Brockhaus, Sep 15 2009

Keywords

• nonn
• easy

Comments

Binomial transform of A165148. Inverse binomial transform of A165150.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (14,-45).

Crossrefs

Cf. A165148, A165150.

Programs

Magma

[ (3*9^n-5^n)/2: n in [0..18] ];

Maple

A165149:=n->(3*9^n-5^n)/2; seq(A165149(n), n=0..30); # Wesley Ivan Hurt, Dec 10 2013

Mathematica

Table[(3*9^n - 5^n)/2, {n, 0, 30}] (* Wesley Ivan Hurt, Dec 10 2013 *)

Formula

a(n) = 14*a(n-1) - 45*a(n-2) for n > 1; a(0) = 1, a(1) = 11.

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

E.g.f.: exp(5*x)*(3*exp(4*x) - 1)/2. - Stefano Spezia, Mar 21 2023