The maximal number of regions into which space can be divided by planes is
(Yaglom and Yaglom 1987, pp. 102-106). For , 2, ..., these give the values 2, 4, 8, 15, 26, 42, ...
(OEIS A000125), a sequence whose values are
sometimes called the "cake numbers" due
to their relation to the cake cutting problem. This
is the same solution as for cylinder cutting.