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Why is Schröder numbers equivalent to the number of perfect matchings for triangular grid of n squares and how the graph look like? [duplicate]
In the OEIS entry for the Schröder numbers is A006318. There is a comment which related the sequence to perfect matchings:
The number of perfect matchings in a triangular grid of n squares (n = 1, 4, ...
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Why is the number of Perfect Matchings in a triangular grid equivalent to the number of Royal Paths?
The sequence A006318 at OEIS stands for the Schröder numbers.
They describes the number of lattice paths from the southwest corner $(0,0)$ of an $n\times n$ grid to the northeast corner $(n,n)$, ...
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