  We study generating functions for the number of involutions in $S_n$ avoiding
(or containing once) 132, and avoiding (or containing once) an arbitrary
permutation $\tau$ on $k$ letters. In several interesting cases the generating
function depends only on $k$ and is expressed via Chebyshev polynomials of the
second kind. In particular, we establish that involutions avoiding both 132 and
$12... k$ have the same enumerative formula according to the length than
involutions avoiding both 132 and any {\em double-wedge pattern} possibly
followed by fixed points of total length $k$. Many results are also shown with
a combinatorial point of view.
