A083226 a(n) = (8*9^n + (-9)^n)/9.

1, 7, 81, 567, 6561, 45927, 531441, 3720087, 43046721, 301327047, 3486784401, 24407490807, 282429536481, 1977006755367, 22876792454961, 160137547184727, 1853020188851841, 12971141321962887, 150094635296999121

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Index entries for linear recurrences with constant coefficients, signature (0,81).

Formula

a(n) = (8*9^n + (-9)^n)/9.

G.f.: (1+7*x)/((1+9*x)*(1-9*x)).

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

a(n) = 81*a(n-2); a(0)=1, a(1)=7. - Harvey P. Dale, May 24 2012

Mathematica

Table[(8*9^n+(-9)^n)/9, {n, 0, 20}] (* or *) LinearRecurrence[{0, 81}, {1, 7}, 20] (* Harvey P. Dale, May 24 2012 *)

Prog

(Magma) [(8*9^n+(-9)^n)/9: n in [0..25]]; // Vincenzo Librandi, Jun 29 2011
(PARI) a(n)=(8*9^n+(-9)^n)/9 \\ Charles R Greathouse IV, Jun 29 2011

Crossrefs

Cf. A083225, A083227.

Sequence in context: A058785 A171768 A050861 * A088735 A364322 A339710

Adjacent sequences: A083223 A083224 A083225 * A083227 A083228 A083229

Keyword

easy,nonn

Author

Paul Barry, Apr 23 2003

Status

approved