Uniform recurrence in the Motzkin numbers and related sequences mod \(p\)
The electronic journal of combinatorics, Tome 32 (2025) no. 2
Many famous integer sequences, including the Catalan numbers and the Motzkin numbers, can be expressed as the constant terms of the polynomials $P(x)^nQ(x)$ for some Laurent polynomial $Q$, and symmetric Laurent trinomial $P$. In this paper, we characterize the primes for which sequences of this form are uniformly recurrent modulo $p$. For all other primes, we show that the set of indices for which our sequences are congruent to $0$ has density $1$. This is accomplished by showing that the study of these sequences mod $p$ can be reduced to the study of the generalized central trinomial coefficients, which are well-behaved mod $p$.
DOI :
10.37236/13089
Classification :
11B50, 68R15, 05A15, 11B85
Affiliations des auteurs :
Nadav Kohen 1
@article{10_37236_13089,
author = {Nadav Kohen},
title = {Uniform recurrence in the {Motzkin} numbers and related sequences mod \(p\)},
journal = {The electronic journal of combinatorics},
year = {2025},
volume = {32},
number = {2},
doi = {10.37236/13089},
zbl = {8062178},
url = {http://geodesic.mathdoc.fr/articles/10.37236/13089/}
}
Nadav Kohen. Uniform recurrence in the Motzkin numbers and related sequences mod \(p\). The electronic journal of combinatorics, Tome 32 (2025) no. 2. doi: 10.37236/13089
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