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

Offset

0,2

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).

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

Mathematica

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

Prog

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

Crossrefs

Cf. A118004, A016185.

Sequence in context: A261741 A228414 A043042 * A229281 A144071 A366596

Adjacent sequences: A191462 A191463 A191464 * A191466 A191467 A191468

Keyword

nonn,easy

Author

Vincenzo Librandi, Jun 03 2011

Status

approved