  Babson and Steingr\'{\i}msson introduced generalized permutation patterns
that allow the requirement that two adjacent letters in a pattern must be
adjacent in the permutation. Claesson presented a complete solution for the
number of permutations avoiding any single pattern of type $(1,2)$ or $(2,1)$.
For eight of these twelve patterns the answer is given by the Bell numbers. For
the remaining four the answer is given by the Catalan numbers. With respect to
being equidistributed there are three different classes of patterns of type
$(1,2)$ or $(2,1)$. We present a recursion for the number of permutations
containing exactly one occurrence of a pattern of the first or the second of
the aforementioned classes, and we also find an ordinary generating function
for these numbers. We prove these results both combinatorially and
analytically. Finally, we give the distribution of any pattern of the third
class in the form of a continued fraction, and we also give explicit formulas
for the number of permutations containing exactly $r$ occurrences of a pattern
of the third class when $r\in\{1,2,3\}$.
