OFFSET
1,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..200
Index entries for linear recurrences with constant coefficients, signature (15,-27,13).
FORMULA
a(n) = 15*a(n-1)-27*a(n-2)+13*a(n-3), with a(1)=1, a(2)=15, a(3)=198. - Vincenzo Librandi, Oct 20 2012
G.f.: x/((1-13*x)*(1-x)^2). - Jinyuan Wang, Mar 11 2020
MAPLE
a:=n->sum((13^(n-j)-1)/12, j=0..n): seq(a(n), n=1..17); # Zerinvary Lajos, Jan 05 2007
a:= n-> (Matrix([[1, 0, 1], [1, 1, 1], [0, 0, 13]])^n)[2, 3]:
seq(a(n), n=1..17); # Alois P. Heinz, Aug 06 2008
MATHEMATICA
LinearRecurrence[{15, -27, 13}, {1, 15, 198}, 20] (* Vincenzo Librandi, Oct 20 2012 *)
PROG
(Magma) I:=[1, 15, 198]; [n le 3 select I[n] else 15*Self(n-1) - 27*Self(n-2)+ 13*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 20 2012
(Maxima)
a[1]:1$
a[2]:15$
a[3]:198$
a[n]:=15*a[n-1]-27*a[n-2]+13*a[n-3]$
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved