  Several authors have examined connections among restricted permutations,
continued fractions, and Chebyshev polynomials of the second kind. In this
paper we prove analogues of these results for involutions which avoid 3412. Our
results include a recursive procedure for computing the generating function for
involutions which avoid 3412 and any set of additional patterns. We use our
results to give enumerations and generating functions for involutions which
avoid 3412 and various sets of additional patterns. In many cases we express
these generating functions in terms of Chebyshev polynomials of the second
kind.
