On the characterization of periodic complex Horadam sequences

Journal article


Bagdasar, Ovidiu and Larcombe, Peter J. 2013. On the characterization of periodic complex Horadam sequences. Fibonacci Quarterly.
AuthorsBagdasar, Ovidiu and Larcombe, Peter J.
Abstract

Horadam sequences are second-order linear recurrence sequences which depend on a family of four parameters (two in the defining recursion itself, and two initial values). In this article we find necessary and sufficient conditions for the periodicity of complex Horadam sequences, under general initial values, characterizing sequence behavior for degenerate and non-degenerate characteristic solution types. Inner and outer boundaries for regions containing periodic orbits are also determined.

KeywordsRecurrent sequences; Fibonacci numbers; Periodic sequences
Year2013
JournalFibonacci Quarterly
PublisherFibonacci Association
ISSN0015-0517
Web address (URL)http://hdl.handle.net/10545/620939
http://creativecommons.org/licenses/by/4.0/
hdl:10545/620939
Publication dates01 Feb 2013
Publication process dates
Deposited21 Nov 2016, 16:07
ContributorsUniversity of Derby
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Larcombe, Peter J. and Fennessey, Eric J. 2014. A non-linear identity for a particular class of polynomial families. Fibonacci Quarterly.
On cyclicity and density of some Catalan polynomial sequences
Larcombe, Peter J. and Fennessey, Eric J. 2014. On cyclicity and density of some Catalan polynomial sequences. Bulletin of the Institute of Combinatorics and its Applications (ICA).
Some factorisation and divisibility properties of Catalan polynomials
Jarvis, Frazer A., Larcombe, Peter J. and Fennessey, Eric J. 2014. Some factorisation and divisibility properties of Catalan polynomials. Bulletin of the Institute of Combinatorics and its Applications (ICA).
Generalised Catalan polynomials and their properties
Larcombe, Peter J., Jarvis, Frazer A. and Fennessey, Eric J. 2014. Generalised Catalan polynomials and their properties. Bulletin of the Institute of Combinatorics and its Applications (ICA).
The Asymptotic Form of the Sum $\sum_{i=0}^{n} i^{p} { n+i \choose i }$: Two Proofs
Larcombe, Peter J., Kirschenhofer, Peter and Fennessey, Eric J. 2014. The Asymptotic Form of the Sum $\sum_{i=0}^{n} i^{p} { n+i \choose i }$: Two Proofs. Utilitas Mathematica.
On some functions involving the lcm and gcd of integer tuples
Bagdasar, Ovidiu 2014. On some functions involving the lcm and gcd of integer tuples. Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informatics and mechanics. https://doi.org/10.5937/SPSUNP1402091B