OFFSET
0,2
COMMENTS
Pisano period lengths: 1, 1, 8, 1, 24, 8, 3, 2, 24, 24, 15, 8, 168, 3, 24, 2, 4, 24, 120, 24, ... - R. J. Mathar, Aug 10 2012
LINKS
Vincenzo Librandi and Harvey P. Dale, Table of n, a(n) for n = 0..1000 (Vincenzo Librandi to 177)
Index entries for linear recurrences with constant coefficients, signature (2,7).
FORMULA
a(n) = 2*a(n-1) + 7*a(n-2) for n > 1; a(0) = 1, a(1) = 13.
G.f.: (1+11*x)/(1-2*x-7*x^2).
a(n) = ((1+3*sqrt(2))*(1+2*sqrt(2))^n + (1-3*sqrt(2))*(1-2*sqrt(2))^n)/2.
MATHEMATICA
LinearRecurrence[{2, 7}, {1, 13}, 50] (* Harvey P. Dale, Oct 16 2011 *)
PROG
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+3*r)*(1+2*r)^n+(1-3*r)*(1-2*r)^n)/2: n in [0..23] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 20 2009
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Aug 15 2009
EXTENSIONS
Edited and extended beyond a(5) by Klaus Brockhaus, Aug 20 2009
STATUS
approved