Let $S$ be a set, and let $\{x_i\},\ i=0,1,2,\dots$ and $\{y_i\},\ i=0,1,2,\dots$ be two sequences in $S$ . The interleave sequence is defined to be the sequence $x_0, y_0, x_1, y_1, \dots$ . Formally, it is the sequence $\{z_i\},\ i=0,1,2,\dots$ given by $$ z_i := \begin{cases} x_k & \text{\ \ if } i=2k \text{ is even,}\\ y_k & \text{\ \ if } i=2k+1 \text{ is odd.} \end{cases} $$