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Recently, a new class of words, denoted by L_n, was shown to be in bijectionwith a subset of the Dyck paths of length 2n having cardinality given by the(n-1)-st Catalan number. Here, we consider statistics on L_n recording thenumber of occurrences of a letter i. In the cases i = 0 and i = 1, we are ableto determine explicit expressions for the number of members of L_n containing agiven number of zeros or ones, which generalizes the prior result. To do so, wemake use of recurrences to derive a functional equation satisfied by thegenerating function, which we solve by a new method employing Chebyshevpolynomials. Recurrences and generating function formulas are also provided inthe case of general i.

Chebyshev Polynomials and Statistics on a New Collection of Words in the Catalan Family