Let n be the number of straight cuts to be made on a 2D pie, then the number of slices can be given by:

Slices=No.of touchpoints+(No.of intersections-previous lines) where

No.of touchpoints=No.of cuts*2 (points where the lines touch the circumference)

No.of intersections=No.of points within the pie where 2 lines cross each other

No.of previous lines=n-1

and No.of intersections=(n-1*(n))/2

The closed form function= (n*2)+((n*(n-1)/2)-(n-1))