  A permutation is said to be \emph{alternating} if it starts with rise and
then descents and rises come in turn. In this paper we study the generating
function for the number of alternating permutations on $n$ letters that avoid
or contain exactly once 132 and also avoid or contain exactly once an arbitrary
pattern on $k$ letters. In several interesting cases the generating function
depends only on $k$ and is expressed via Chebyshev polynomials of the second
kind.
