A191465 a(n) = 9^n - 2^n.

0, 7, 77, 721, 6545, 59017, 531377, 4782841, 43046465, 387419977, 3486783377, 31381057561, 282429532385, 2541865820137, 22876792438577, 205891132061881, 1853020188786305, 16677181699535497, 150094635296736977, 1350851717672467801, 12157665459055880225, 109418989131510262057

Offset: 0

Author

Vincenzo Librandi, Jun 03 2011

Keywords

• nonn
• easy

Comments

a(n) is the number of words of length n over the alphabet {1,2,...,9} where at least one letter >= 3 appears. - Joerg Arndt, Jan 18 2024

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Index entries for linear recurrences with constant coefficients, signature (11,-18).

Crossrefs

Cf. A016133, A016185, A118004.

Programs

Mathematica

Table[9^n-2^n,{n,0,20}] (* Harvey P. Dale, Apr 16 2014 *)

PARI

a(n)=9^n-1<Charles R Greathouse IV, Jun 08 2011

Formula

a(n) = 11*a(n-1) - 18*a(n-2).

G.f.: 7*x/((1-2*x)*(1-9*x)). - Vincenzo Librandi, Oct 04 2014

a(n) = 7*A016133(n-1). - R. J. Mathar, Mar 10 2022

E.g.f.: 2*exp(11*x/2)*sinh(7*x/2). - Elmo R. Oliveira, Mar 31 2025