Difference equations with delay

In this note we employ combinatorial arguments to count and classify certain periodic solutions of the delayed difference equation x(n) = f(x(n - k)), with k greater than or equal to 2 given and n is an element of Z. The periodic solutions that we consider are formed by combining k copies of an m-periodic solution of the "ordinary" difference equation x(n) = f(x(n - 1)). We also briefly discuss the possibility of braiding different periodic solutions of the ordinary difference equation into a periodic solution of the delayed version.