  We consider the problem of enumerating the permutations containing exactly
$k$ occurrences of a pattern of length 3. This enumeration has received a lot
of interest recently, and there are a lot of known results. This paper presents
an alternative approach to the problem, which yields a proof for a formula
which so far only was conjectured (by Noonan and Zeilberger). This approach is
based on bijections from permutations to certain lattice paths with ``jumps'',
which were first considered by Krattenthaler.
