This material has been published in Electron. J. Combin. 18(2) (2012), Article P37, 83 pp, the only definitive repository of the content that has been certified and accepted after peer review.

Manuel Kauers, Christian Krattenthaler and Thomas W. Müller

A method for determining the mod-2k behaviour of recursive sequences, with applications to subgroup counting

(66 pages)

Abstract. We present a method to obtain congruences modulo powers of 2 for sequences given by recurrences of finite depth with polynomial coefficients. We apply this method to Catalan numbers, Fuß-Catalan numbers, and to subgroup counting functions associated with Hecke groups and their lifts. This leads to numerous new results, including many extensions of known results to higher powers of 2.

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