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Looking for a formula that counts the number of unique constructions of "coffee tables" that have an n-gon tabletop.
Coffee tables are build by placing legs under vertices of an n-gon in such a way that the table won't tip over. Here are the rules:
If n is even we can use (2, ..., n) legs. Every valid table must ...
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Number of ways to connect sets of $k$ dots in a perfect $n$-gon
Let $Q(n,k)$ be the number of ways in which we can connect sets of $k$ vertices in a given perfect $n$-gon such that no two lines intersect at the interior of the $n$-gon and no vertex remains ...
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