Difference equations with delay

In this note we employ combinatorial arguments to count and classify certai n 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 peri odic solutions that we consider are formed by combining k copies of an m-pe riodic solution of the "ordinary" difference equation x(n) = f(x(n - 1)). W e also briefly discuss the possibility of braiding different periodic solut ions of the ordinary difference equation into a periodic solution of the de layed version.