MathDB
Covering with domino tiles

Source: Rioplatense L-2 2022 #6

December 13, 2022
combinatorics

Problem Statement

Let N(a,b)N(a,b) be the number of ways to cover a table a×ba \times b with domino tiles. Let M(a,2b+1)M(a,2b+1) be the number of ways to cover a table a×2b+1a \times 2b+1 with domino tiles, such that there are no vertical tile in the central column. Prove that M(2m,2n+1)=2m⋅N(2m,n)⋅N(2m,n−1)M(2m,2n+1)=2^m \cdot N(2m,n)\cdot N(2m,n-1)
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