Let an denote the number of ways to triangulate a convex polygon with n+ 2 sides,...

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Let an denote the number of ways to triangulate a convex polygon with n+ 2 sides, with vertices labeled ..., n+2, into triangles with non-intersecting diagonals. Two triangulations are considered equivalent if they consist of the same set of diagonals. 1, 2,.. For example, there are two distinct dissections of a 4-gon with vertices labeled 1, 2, 3, 4 into triangles with non-intersecting diagonals, as shown below. Thus, we conclude that a2 = 2. 2 1 АЙ 3 4 1 4 Here is an example of one such triangulation of a hexagon: Find an for n= 1, 2, 3, 4. 2 3 Let an denote the number of ways to triangulate a convex polygon with n+ 2 sides, with vertices labeled ..., n+2, into triangles with non-intersecting diagonals. Two triangulations are considered equivalent if they consist of the same set of diagonals. 1, 2,.. For example, there are two distinct dissections of a 4-gon with vertices labeled 1, 2, 3, 4 into triangles with non-intersecting diagonals, as shown below. Thus, we conclude that a2 = 2. 2 1 АЙ 3 4 1 4 Here is an example of one such triangulation of a hexagon: Find an for n= 1, 2, 3, 4. 2 3