Originally posted by Acolyte
x(0) = 1
x(1) = 2
x(2) = 7
x(3) = 2
I believe this is the unique answer of period 4 s.t. x(0) = 1.
Let me guess: a further problem is to find the solution such that x(0) = 1, x(n) > x(n-1) for all n (which incidentally gives all solution sequences containing 1). It would indeed be interesting if this was an integer sequence.
The cardinal rule of exams is that when one's answer is an integer (or a periodic sequence of them!) one is supposed to be confident in one's rightness
Actually, you can solve your problem if you haven't already by looking at the two simpler relations which can hold if the first condition does. One is that x(n) = x(n-2). What is the other?
Well done, BTW. This was the last bit of a STEP question; we had to prove a few preliminaries, find this sequence, and show it to be unique.