Periodic sequences are sequences for which there is some integer N for which, for all n > N, a(n) = a(n - N). (More generally, if the sequence does not start at 1 but at k, this holds for all n > N + k - 1.) The number N is called the period of the sequence. Sequences which are periodic beyond some point are called eventually periodic.
All periodic sequences are linear recurrence relations of order at most N.