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Recently, Babson and Steingrimsson (see [BS]) introduced generalized permutations patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. We study generating functions for the number of permutations on letters avoiding (or containing exactly once) and an arbitrary generalized pattern on letters, or containing exactly once. In several cases the generating function depends only on and is expressed via Chebyshev polynomials of the second kind, and generating function of Motzkin numbers.

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