Arithmetic of Some Sequences Via $2$-determinants
Combinatorics
2021-05-12 v4
Abstract
We extend our investigation of -determinants, which we defined in a previous paper. For a linear homogenous recurrence of the second order, we consider relations between different sequences satisfying the same linear homogeneous recurrence of the second order. After we prove a generalized identity of d'Ocagne, we derive, from a single identity, a number of classical identities (and their generalizations) such as d'Ocagne's, Cassini's, Catalan's and Vajda's. Along the way, the corresponding combinatorial interpretations in terms of restricted words over a finite alphabet are stated for the sequences we investigate.
Cite
@article{arxiv.2008.13200,
title = {Arithmetic of Some Sequences Via $2$-determinants},
author = {Dusko Bogdanic and Milan Janjic},
journal= {arXiv preprint arXiv:2008.13200},
year = {2021}
}