equilateral triangle
Source: Canada 2005
June 26, 2009
combinatorics proposedcombinatorics
Problem Statement
An equilateral triangle of side length is divided into unit triangles. Let be the number of paths from the triangle in the top row to the middle triangle in the bottom row, such that adjacent triangles in a path share a common edge and the path never travels up (from a lower row to a higher row) or revisits a triangle. An example is shown on the picture for n \equal{} 5. Determine the value of .