Problem

Source: China Northern MO 2008 p7 CNMO

Tags: geometry, combinatorics, combinatorial geometry



Given an equilateral triangle lattice composed of $\frac{n(n+1)}{2}$ points (as shown in the figure), record the number of equilateral triangles with three points in the lattice as vertices as $f(n)$. Find an expression for $f(n)$.