Abstract
We study the distribution of the last symbol statistics on the sets of Catalan words avoiding a consecutive pattern of length at most three. For each pattern p, we provide a bivariate generating function, where the coefficient cp(n,k) of xnyk in its series expansion is the number of length n Catalan words avoiding p and ending with the symbol k. We deduce recurrence relations or closed forms for cp(n, k) and we provide asymptotic approximations for the expectation of the last symbol on all Catalan words avoiding p. Finally, we characterize the sequence cp(n, k) using Riordan arrays.
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