OFFSET
1,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..200
Index entries for linear recurrences with constant coefficients, signature (14,-25,12).
FORMULA
a(n) = 14*a(n-1)-25*a(n-2)+12*a(n-3), with a(1)=1, a(2)=14, a(3)=171. - Vincenzo Librandi, Oct 20 2012
G.f.: x/((1-12*x)*(1-x)^2). - Jinyuan Wang, Mar 11 2020
MAPLE
a:=n->sum((12^(n-j)-1^(n-j))/11, j=0..n): seq(a(n), n=1..17); # Zerinvary Lajos, Jan 12 2007
a:= n-> (Matrix([[1, 0, 1], [1, 1, 1], [0, 0, 12]])^n)[2, 3]:
seq(a(n), n=1..17); # Alois P. Heinz, Aug 06 2008
MATHEMATICA
LinearRecurrence[{14, -25, 12}, {1, 14, 171}, 201] (* Vincenzo Librandi, Oct 20 2012 *)
PROG
(Magma) I:=[1, 14, 171]; [n le 3 select I[n] else 14*Self(n-1) - 25*Self(n-2)+ 12*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 20 2012
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved