Question 6
A non-degenerate triangle is formed by three points that are not collinear. A triangle is called *nice* if it is non-degenerate and its vertices have integer coordinates $(x, y)$ such that $0 \le x \le 2018$ and $0 \le y \le 2018$. Let $V_n$ denote the number of nice isosceles triangles for which the coordinates of each vertex satisfy $y \le n$. Prove that
$$
V_{n+1} = 2V_n - 2V_{n-2} + V_{n-3} \quad \text{for all } n \gt 2018^2.
$$
$$
V_{n+1} = 2V_n - 2V_{n-2} + V_{n-3} \quad \text{for all } n \gt 2018^2.
$$