P+N+1

This formula allows one to count the number of regions when number of points of intersection, number of lines are given on an enclosed surface. So both pizza slicing and moser's circle problem can be solved by this. It's easy to observe that in pizza slicing P is C(n,2), N is n. So number of slices are C(n,2)+n+1 and for the moser's circle P is C(n,4), N is C(n,2). Therefore the formula is C(n,4)+C(n,2)+1