OFFSET
0,3
COMMENTS
Pisano period lengths: 1, 1, 3, 2, 8, 3, 48, 2, 3, 8, 110, 6, 168, 48, 24, 4, 8, 3, 45, 8, ... - R. J. Mathar, Aug 10 2012
This is the Lucas sequence U(5,-2). - Bruno Berselli, Jan 08 2013
For n > 0, a(n) equals the number of words of length n-1 over {0,1,...,6} in which 0 and 1 avoid runs of odd lengths. - Milan Janjic, Jan 08 2017
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Wikipedia, Lucas sequence: Specific names.
Index entries for linear recurrences with constant coefficients, signature (5,2).
FORMULA
a(n) = 5*a(n-1) + 2*a(n-2) with n > 1, a(0)=0, a(1)=1.
MATHEMATICA
LinearRecurrence[{5, 2}, {0, 1}, 30] (* Vincenzo Librandi, Nov 12 2012 *)
PROG
(Sage) [lucas_number1(n, 5, -2) for n in range(0, 22)] # Zerinvary Lajos, Apr 24 2009
(Magma) [n le 2 select n-1 else 5*Self(n-1)+2*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 12 2012
(PARI) x='x+O('x^30); concat([0], Vec(x/(1-5*x-2*x^2))) \\ G. C. Greubel, Jan 01 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved