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Number of diagonal-quadrangles

Source: Austrian-Polish 2005, Problem 1

July 5, 2015
EnumerationcombinatoricsPolygons

Problem Statement

For a convex nn-gon PnP_n, we say that a convex quadrangle QQ is a diagonal-quadrangle of PnP_n, if its vertices are vertices of PnP_n and its sides are diagonals of PnP_n. Let dnd_n be the number of diagonal-quadrangles of a convex nn-gon. Determine dnd_n for all n≥8n\geq 8.
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