Interleave sequence

In mathematics, an interleave sequence is obtained by merging two sequences via an in shuffle.

Let ${\displaystyle S}$ be a set, and let ${\displaystyle (x_{i})}$ and ${\displaystyle (y_{i})}$, ${\displaystyle i=0,1,2,\ldots ,}$ be two sequences in ${\displaystyle S.}$ The interleave sequence is defined to be the sequence ${\displaystyle x_{0},y_{0},x_{1},y_{1},\dots .}$ Formally, it is the sequence ${\displaystyle (z_{i}),i=0,1,2,\ldots }$ given by

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