A155663 a(n) = 9^n + 8^n - 1.

1, 16, 144, 1240, 10656, 91816, 793584, 6880120, 59823936, 521638216, 4560526224, 39970994200, 351149013216, 3091621642216, 27274838966064, 241075504183480, 2134495165562496, 18928981513351816, 168109033806481104, 1494966905748847960, 13310586963663775776

Offset: 0

Author

Mohammad K. Azarian, Jan 31 2009

Keywords

• nonn
• easy

Links

• Paolo Xausa, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (18,-89,72).

Crossrefs

Cf. A155646, A155647, A155648, A155649, A155650, A155651, A155652, A155653, A155654, A155655, A155656, A155657, A155658, A155659, A155660, A155661, A155662.

Programs

Mathematica

Table[9^n+8^n-1,{n,0,20}] (* or *) LinearRecurrence[{18,-89,72},{1,16,144},20] (* Harvey P. Dale, Jun 14 2016 *)

PARI

a(n)=9^n+8^n-1 \\ Charles R Greathouse IV, Jun 11 2015

Formula

G.f.: 1/(1-9*x)+1/(1-8*x)-1/(1-x).

E.g.f.: exp(9*x)+exp(8*x)-exp(x).

a(n) = 17*a(n-1)-72*a(n-2)-56 with a(0) = 1, a(1) = 16. - Vincenzo Librandi, Jul 21 2010