A Nameless Number
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Len Smiley  
Trianglefree polygon dissections are a variant of the dissection questions of Catalan, Schroeder, and others: In a convex (n+2)gon with n+2 labeled nodes, what is a(n), the number of ways of drawing nonintersecting diagonals so that no triangles are formed? This question resonates somewhat with the parallel universe of "trianglefree graphs." With a formulation using geometric recurrences, and Mathematica code for the sequence of the number of (noncrossing) diagonal placements in the (n+3)gon with vertices 1, 2, ..., n+3 such that no triangles appear.  


Levels:  High School (912), College 
Languages:  English 
Resource Types:  Problems/Puzzles 
Math Topics:  Constructions, Triangles and Other Polygons, Sequences and Sets 
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