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What Triangles Are in the Triangle?

Consider the triangular grid formed by dividing one equilateral triangle into a grid of equilateral subtriangles in such a way that there are in the base. We want to know which and how many subtriangles there are within this grid. It is a very interesting exercise, involving discrete mathematics tools, to derive the formula for the total number, which is .

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 Jaime Rangel-Mondragon
"What Triangles Are in the Triangle?"
 http://demonstrations.wolfram.com/WhatTrianglesAreInTheTriangle/
 Wolfram Demonstrations Project
 Published: August 6, 2012
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