OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (8,-13,6).
FORMULA
From Vincenzo Librandi, Jun 16 2013: (Start)
G.f.: (1-3*x+7*x^2)/((1-6*x)*(1-x)^2).
a(n) = 8*a(n-1) - 13*a(n-2) + 6*a(n-3). (End)
E.g.f.: exp(x)*(exp(5*x) - x). - Elmo R. Oliveira, Sep 10 2024
MATHEMATICA
Table[6^n - n, {n, 0, 30}] (* or *) CoefficientList[Series[(1 - 3 x + 7 x^2) / ((1 - 6 x) (1 - x)^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jun 16 2013 *)
PROG
(Magma) [6^n-n: n in [0..25]]; // Vincenzo Librandi, Jul 03 2011
(Magma) I:=[1, 5, 34]; [n le 3 select I[n] else 8*Self(n-1)-13*Self(n-2)+6*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 16 2013
(PARI) a(n)=6^n-n \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved