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

2013/08/13 by Christian Krattenthaler, Krattenthaler, Christian, Thomas W. Müller +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Primary 05A15 #Secondary 05E99 11A07 20E06 20E07 68W30 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1308.2856

openalex publication_date 2013/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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