A155614 9^n - 3^n + 1.

1, 7, 73, 703, 6481, 58807, 530713, 4780783, 43040161, 387400807, 3486725353, 31380882463, 282429005041, 2541864234007, 22876787671993, 205891117745743, 1853020145805121, 16677181570526407, 150094634909578633

Offset: 0

Author

Mohammad K. Azarian, Jan 26 2009

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (13,-39,27).

Crossrefs

Cf. A155599, A155600, A155601, A155602, A155603, A155604, A155605, A155606, A155607, A155608, A155609, A155610, A155611, A155612, A155613.

Programs

Mathematica

Table[9^n-3^n+1,{n,0,20}]  (* Harvey P. Dale, Feb 03 2011 *)

PARI

a(n)=9^n-3^n+1 \\ Charles R Greathouse IV, Oct 07 2015

Formula

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

E.g.f.: e^(9*x)-e^(3*x)+e^x.

a(n) = 12*a(n-1)-27*a(n-2)+16 with a(0)=1, a(1)=7. - Vincenzo Librandi, Jul 21 2010