The pancake-cutting problem is to determine the maximum number of pieces into which a pancake can be divided by straight cuts with a knife. The existing cuts divide a new cut into segments, each of which divides an existing piece into two pieces. Therefore, , with initial condition . Using Mathematica’s RSolve function, we see that the number of pancake pieces after cuts is .
M. Gardner, Martin Gardner’s New Mathematical Diversions from Scientific American, New York: Simon and Schuster, 1966, pp. 235–239.
F. S. Roberts, Applied Combinatorics, New Jersey: Prentice-Hall, 1984, pp. 198–200.