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In mathematics, an interleave sequence is obtained by merging two sequences via an in shuffle.
Let S {\displaystyle S} be a set, and let {\displaystyle } and {\displaystyle } , i = 0 , 1 , 2 , … , {\displaystyle i=0,1,2,\ldots ,} be two sequences in S . {\displaystyle S.} The interleave sequence is defined to be the sequence x 0 , y 0 , x 1 , y 1 , … . {\displaystyle x_{0},y_{0},x_{1},y_{1},\dots.} Formally, it is the sequence , i = 0 , 1 , 2 , … {\displaystyle ,i=0,1,2,\ldots } given by