Maximize the number of pieces with n cuts.
1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56
https://oeis.org/A000124 If the smallest pieces have maximal area, how many equal area smallest pieces are there? I get 4, 5, 10, 12, 13, 16, 21 pieces. But I'm going to assume that at least one of these solutions is improvable.