Permutations containing a pattern exactly once and avoiding at least two patterns of three letters

In this paper, we find an explicit formulas, or recurrences, in terms of generating functions for the cardinalities of the sets S-n(T; tau) of all permutations in S-n that contain tau is an element of S-k exactly once and avoid a subset T subset of or equal to S-3 where \T\ greater than or equal to 2.