A155666 a(n) = 9^n - 8^n + 1.

1, 2, 18, 218, 2466, 26282, 269298, 2685818, 26269506, 253202762, 2413042578, 22791125018, 213710059746, 1992110014442, 18478745943858, 170706760005818, 1571545212141186, 14425381885981322, 132080236787517138, 1206736529597136218, 11004743954450081826, 100195617094657583402

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, A155663, A155664, A155665.

Programs

Mathematica

Table[9^n-8^n+1,{n,0,20}] (* or *) LinearRecurrence[{18,-89,72},{1,2,18},20] (* Harvey P. Dale, Aug 16 2015 *)

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) = 2. - Vincenzo Librandi, Jul 21 2010