Christian Krattenthaler and Thomas W. Müller

A method for determining the mod-3k behaviour of recursive sequences

(65 pages)

Abstract. We present a method for obtaining congruences modulo powers of 3 for sequences given by recurrences of finite depth with polynomial coefficients. We apply this method to Catalan numbers, Motzkin numbers, Riordan numbers, Schröder numbers, Eulerian numbers, trinomial coefficients, Delannoy numbers, and to functions counting free subgroups of finite index in the inhomogeneous modular group and its lifts. This leads to numerous new results, including many extensions of known results to higher powers of 3.

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The paper is accompanied by the following Mathematica files: By using the notebook (which requires the other file as input file ), you are able to redo (most of) the computations that are presented in this article.
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