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arXiv · 1703.00826

Structure and asymptotics for Motzkin numbers modulo primes using automata

Rob Burns
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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.

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Rob Burns. 2017-03-02. Structure and asymptotics for Motzkin numbers modulo primes using automata. https://arxiv.org/abs/1703.00826

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