OFFSET
1,1
COMMENTS
Consider the 4-step recursion x(k) = (x(k-1) + x(k-2) + x(k-3) + x(k-4)) mod n. For any of the n^4 initial conditions x(1), x(2), x(3) and x(4) in Zn, the recursion has a finite period. When n is a prime in this sequence, all of the orbits, except the one containing (0,0,0,0), have the same length.
For the prime 3 the orbit structure contains three orbits of length 1: (0,0,0,0), (1,1,1,1) and (2,2,2,2).
LINKS
Eric Weisstein's World of Mathematics, Fibonacci n-Step Number.
CROSSREFS
KEYWORD
nonn
AUTHOR
T. D. Noe, May 02 2005, revised May 12 2005
STATUS
approved