OFFSET
1,2
COMMENTS
Consider the 2-step recursion f(k)=f(k-1)+f(k-2) mod n. For any of the n^2 initial conditions f(1) and f(2) in Zn, the recursion has a finite period. Each of these n^2 vectors belongs to exactly one orbit. In general, there are only a few different orbit lengths for each n. For n=8, there are 4 different lengths: 1, 3, 6 and 12. The maximum possible length of an orbit is A001175(n), the period of the Fibonacci 2-step sequence mod n. - T. D. Noe, May 02 2005
LINKS
B. Avila and T. Khovanova, Free Fibonacci Sequences, arXiv preprint arXiv:1403.4614 [math.NT], 2014 and J. Int. Seq. 17 (2014) # 14.8.5
Eric Weisstein's World of Mathematics, Fibonacci n-Step Number.
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Larry Reeves (larryr(AT)acm.org), Jan 06 2005
STATUS
approved