Problem

Source: India Postal Coaching 2014 Set 5 Problem 3

Tags: combinatorics unsolved, combinatorics



Consider a regular triangular array of $n(n+1)/2$ points.Let $f(n)$ denote the number of equilateral triangles formed by taking some $3$ points in the array as vertices.Prove that $f(n)=\frac{(n-1)n(n+1)(n+2)}{24}$.