(1) Compute the number of isosceles triangles if all vertices are the same. (Note the differences when n is even, odd or a multiple of 3.)

(2) Subtract the no. of triangles formed by mismatched vertices. Start by dividing and counting the "1"/"0" vertices that can be paired.

Note: An isoceles triangle is determined by either 2 vertices, or 1 vertex and a side's length. Be aware of double counting.