OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (11,-19,9).
FORMULA
G.f.: (1+7*x-80*x^2)/((1-x)^2*(1-9*x)).
a(n) = 11*a(n-1) - 19*a(n-2) + 9*a(n-3).
E.g.f.: exp(x)*(exp(8*x) + 9*x). - Elmo R. Oliveira, Sep 09 2024
MATHEMATICA
Table[(9^n + 9 n), {n, 0, 25}] (* or *) CoefficientList[Series[(1 + 7 x - 80 x^2)/((1 - x)^2 (1 - 9 x)), {x, 0, 30}], x]
LinearRecurrence[{11, -19, 9}, {1, 18, 99}, 20] (* Harvey P. Dale, Aug 18 2014 *)
PROG
(Magma) [9^n + 9*n: n in [0..25]]; /* or */ I:=[1, 18, 99]; [n le 3 select I[n] else 11*Self(n-1)-19*Self(n-2)+9*Self(n-3): n in [1..30]];
(PARI) a(n)=9^n+9*n \\ Charles R Greathouse IV, Apr 18 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 03 2013
STATUS
approved