A method for determining the mod-pk behaviour of recursive sequences
Abstract
We present a method for obtaining congruences modulo powers of a prime number~p for combinatorial sequences whose generating function satisfies an algebraic differential equation. This method generalises the one by Kauers and the authors [Electron. J. Combin. 8(2) (2012), Art. P37; arXiv:1107.2015] from p=2 to arbitrary primes. Our applications include congruences for numbers of non-crossing graphs and numbers of Kreweras walks modulo powers of~3, as well as congruences for Fu-Catalan numbers and blossom tree numbers modulo powers of arbitrary primes.
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