Structure and asymptotics for Motzkin numbers modulo primes using automata
Number Theory
2017-03-03 v1
Abstract
We establish a lower bound of 2/p(p-1) for the asymptotic density of the Motzkin numbers divisible by a general prime number p > 3. We provide a criteria for when this asymptotic density is actually 1. We also provide a partial characterisation of those Motzkin numbers which are divisible by a prime p > 3. All results are obtained using the automata method of Rowland and Yassawi.
Cite
@article{arxiv.1703.00826,
title = {Structure and asymptotics for Motzkin numbers modulo primes using automata},
author = {Rob Burns},
journal= {arXiv preprint arXiv:1703.00826},
year = {2017}
}
Comments
21 pages, 4 figures, 6 tables. arXiv admin note: text overlap with arXiv:1612.08146, arXiv:1701.02975