Manuel Kauers, Christian Krattenthaler, T. Mueller,
"A method for determining the mod-$2^k$ behaviour of recursive sequences, with applications to subgroup counting"
, in Electronic Journal of Combinatorics, Vol. 18, Nummer 2, Seite(n) 1-76, 2012, ISSN: 1077-8926
A method for determining the mod-$2^k$ behaviour of recursive sequences, with applications to subgroup counting
Sprache des Titels:
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, Fu\ss--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 $2$.