Year: 2025
Type: article
Abstract: The Horadam sequence {Hn(a,b;p,q)}n⩾0 has been widely studied in combinatorics and number theory. In this paper, we find that the context-free grammar G={x→px+y,y→qx} can be used to generate Horadam sequences. Using this grammar, we deduce several identities, including Cassini-like identities. Moreover, we investigate the relationship between two distinct Horadam sequences Hn(a,b;p,q) and Hn(c,d;p,q) with (a,b)≠(c,d) and provide an approach to derive identities, which can be illustrated by the Fibonacci and Lucas sequences as well as the two kinds of Chebyshev polynomials.
Source: Axioms
Authors: Jun-Ying Liu, Hai-Ling Li, Zhi-Hong Zhang
Institution: Shandong University of Technology
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
Award: 组合统计量与构造性组合方法的研究
OpenAlex ID: W4415823664