OEIS A000150: Rooted asymmetric polygon dissections

We examine A000150, the count of ways to dissect an n-gon into triangles with a distinguished exterior edge, counting dissections that are asymmetric about that edge. We trace its connections to Dick paths with an odd number of peaks at even height, and to unordered binary trees with non-identical left and right subtrees. We explore how Catalan numbers enter via their generating function, the asymptotic growth a_n ~ 2^{2n-1}/(sqrt(pi) n^{3/2}), and discuss practical contexts from triangulation in computer graphics to origami. We’ll also touch on the Linden word links that weave these ideas together.

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