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Triangulation

Source: IMOTC 2014 Practice Test 2 Problem 2

July 11, 2014
AMCUSA(J)MOUSAMOcombinatorics unsolvedcombinatorics

Problem Statement

Let nn be a natural number.A triangulation of a convex n-gon is a division of the polygon into n−2n-2 triangles by drawing n−3n-3 diagonals no two of which intersect at an interior point of the polygon.Let f(n)f(n) denote the number of triangulations of a regular n-gon such that each of the triangles formed is isosceles.Determine f(n)f(n) in terms of nn.
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