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Certain famous combinatorial sequences, such as the Catalan numbers and theMotzkin numbers, when taken modulo a prime power, can be computed by finiteautomata. Many theorems about such sequences can therefore be proved usingWalnut, which is an implementation of a decision procedure for proving variousproperties of automatic sequences. In this paper we explore some results (oldand new) that can be proved using this method.

Congruence properties of combinatorial sequences via Walnut and the Rowland-Yassawi-Zeilberger automaton