I came across this sequence in a programming contest F(n)= F(n-1)-F(n-2); Given F0 and F1 find nth term
(http://codeforces.com/contest/450/problem/B) (the contest is over)
Now the solution of this problem is like this The sequence take value f0, f1, f1-f0, -f0, -f1, f0 - f1 then again f0 and the whole sequence is repeated.
I get that this value is being repeated but could not found the reason for this cyclic order. I searched for cyclic order and sequences but could not find sufficient material that could give the actual feel for the reason of the cycle.