A155593 a(n) = 9^n + 2^n - 1.

1, 10, 84, 736, 6576, 59080, 531504, 4783096, 43046976, 387421000, 3486785424, 31381061656, 282429540576, 2541865836520, 22876792471344, 205891132127416, 1853020188917376, 16677181699797640, 150094635297261264

Offset: 0

Author

Mohammad K. Azarian, Jan 24 2009

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (12,-29,18).

Crossrefs

Cf. A074501, A074600, A005057, A005056, A099393, A155588, A155590, A155592.

Programs

Mathematica

Table[9^n+2^n-1,{n,0,30}] (* or *) LinearRecurrence[{12,-29,18},{1,10,84},30] (* Harvey P. Dale, Sep 09 2022 *)

PARI

a(n)=9^n+2^n-1^n \\ Charles R Greathouse IV, Jun 11 2015

Formula

G.f.: 1/(1-9*x)+1/(1-2*x)-1/(1-x).

E.g.f.: e^(9*x)+e^(2*x)-e^x.

a(n) = 11*a(n-1)-18*a(n-2)-8 with a(0)=1, a(1)=10. - Vincenzo Librandi, Jul 21 2010

a(n) = A074604(n)-1. - R. J. Mathar, Mar 10 2022