A method for deterining the mod-$3^k$ behaviour of recursive sequences
Combinatorics
2013-08-14 v1
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, Schr\"oder 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.
Cite
@article{arxiv.1308.2856,
title = {A method for deterining the mod-$3^k$ behaviour of recursive sequences},
author = {Christian Krattenthaler and Thomas W. Müller},
journal= {arXiv preprint arXiv:1308.2856},
year = {2013}
}
Comments
AmS-LaTeX, 82 pages