  Consider the number of permutations in the symmetric group on n letters that
contain c copies of a given pattern. As c varies (with n held fixed) these
numbers form a sequence whose properties we study for the monotone patterns and
the patterns 1, l, l-1, ..., 2. We show that, except for the patterns 1, 2 and
2, 1 where the sequence is well-known to be log concave, there are infinitely
many n where the sequence has internal zeros.
