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.
method for determining the mod-2k behaviour of
recursive sequences, with applications to subgroup counting
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.
The following versions are available:
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
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