OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (11,-19,9).
FORMULA
From Vincenzo Librandi, Jun 17 2013: (Start)
G.f.: (1-3*x+10*x^2)/((1-9*x)(1-x)^2).
a(n) = 11*a(n-1) - 19*a(n-2) + 9*a(n-3). (End)
E.g.f.: exp(x)*(exp(8*x) - x). - Elmo R. Oliveira, Sep 09 2024
MATHEMATICA
Table[9^n - n, {n, 0, 20}] (* or *) CoefficientList[Series[(1 - 3 x + 10 x^2) / ((1 - 9 x) (1 - x)^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jun 17 2013 *)
PROG
(Magma) [9^n-n: n in [0..25]]; // Vincenzo Librandi, Jul 06 2011
(Magma) I:=[1, 8, 79]; [n le 3 select I[n] else 11*Self(n-1)-19*Self(n-2)+9*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 17 2013
(PARI) a(n)=9^n-n \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved