OFFSET
1,2
COMMENTS
Consider the 5-step recursion x(k)=x(k-1)+x(k-2)+x(k-3)+x(k-4)+x(k-5) mod n. For any of the n^5 initial conditions x(1), x(2), x(3), x(4) and x(5) in Zn, the recursion has a finite period. Each of these n^5 vectors belongs to exactly one orbit. In general, there are only a few different orbit lengths (A106290). For instance, the 1468 orbits mod 8 have lengths of 1, 2, 3, 6, 12 and 24.
LINKS
D. D. Wall, Fibonacci series modulo m, Amer. Math. Monthly, 67 (1960), 525-532.
Eric Weisstein's World of Mathematics, Fibonacci n-Step Number.
CROSSREFS
KEYWORD
nonn
AUTHOR
T. D. Noe, May 02 2005
STATUS
approved