凸n边形的对角线最多能将其内部分成几个区域

https://math.stackexchange.com/questions/3384251/into-how-many-regions-do-the-sides-and-diagonals-of-a-convex-n-gon-divide-the

$$f(n)=f(n-1)+1+(\sum_{i=1}^{n-3}i\times (n-i-2)+1)$$

$$f(n)=\dfrac{(n-1)(n-2)(n^2-3n+12)}{24}$$