OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..300
Index entries for linear recurrences with constant coefficients, signature (14,-25,12).
FORMULA
From Vincenzo Librandi, Jun 17 2013: (Start)
G.f.: (1 - 3*x + 13*x^2)/((1-12*x)*(1-x)^2).
a(n) = 14*a(n-1) - 25*a(n-2) + 12*a(n-3). (End)
E.g.f.: exp(x)*(exp(11*x) - x). - Elmo R. Oliveira, Sep 10 2024
MATHEMATICA
Table[12^n - n, {n, 0, 20}] (* or *) CoefficientList[Series[(1 - 3 x + 13 x^2) / ((1 - 12 x) (1 - x)^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jun 17 2013 *)
PROG
(Magma) [12^n-n: n in [0..20]]; // Vincenzo Librandi, Jul 01 2011
(PARI) a(n)=12^n-n \\ Charles R Greathouse IV, Jul 01 2011
(Magma) I:=[1, 11, 142]; [n le 3 select I[n] else 14*Self(n-1)-25*Self(n-2)+12*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 17 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved