OFFSET
0,2
COMMENTS
After 83, the next prime of this form is a(76). - Bruno Berselli, Jun 18 2013
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..300
Index entries for linear recurrences with constant coefficients, signature (11,-19,9).
FORMULA
G.f.: (-1+x+8*x^2)/((9*x-1)*(x-1)^2).
a(n) = 11*a(n-1) - 19*a(n-2) + 9*a(n-3).
E.g.f.: exp(x)*(exp(8*x) + x). - Elmo R. Oliveira, Sep 09 2024
MATHEMATICA
Table[9^n + n, {n, 0, 30}] (* or *) CoefficientList[Series[(- 1 + x + 8 x^2) / ((9 x - 1) (x - 1)^2), {x, 0, 30}], x]
LinearRecurrence[{11, -19, 9}, {1, 10, 83}, 20] (* Harvey P. Dale, Feb 03 2016 *)
PROG
(Magma) [9^n+n: n in [0..30]]; /* or */ I:=[1, 10, 83]; [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+n \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Jun 16 2013
STATUS
approved