On the geometry of certain periodic non-homogeneous Horadam sequences.

Journal article

Bagdasar, Ovidiu and Popa, Ioan-Lucian 2016. On the geometry of certain periodic non-homogeneous Horadam sequences. Electronic Notes in Discrete Mathematics. https://doi.org/10.1016/j.endm.2016.11.002
AuthorsBagdasar, Ovidiu and Popa, Ioan-Lucian
Abstract

Horadam sequences are second-order recurrences depending on a family of four complex parameters: two initial conditions and two recurrence coefficients. The periodicity conditions, as well as the number and geometric structure of self-repeating Horadam sequences of fixed length have been recently investigated. In this paper various geometric properties of non-homogeneous Horadam sequences are explored, including periodicity conditions and the structure of certain periodic orbits.

Horadam sequences are second-order recurrences depending on a family of four
complex parameters: two initial conditions and two recurrence coefficients. The periodicity
conditions, as well as the number and geometric structure of self-repeating
Horadam sequences of fixed length have been recently investigated. In this paper
various geometric properties of non-homogeneous Horadam sequences are explored,
including periodicity conditions and the structure of certain periodic orbits.

KeywordsRecurrent sequences; Periodic sequences; Geometric patterns
Year2016
JournalElectronic Notes in Discrete Mathematics
PublisherElsevier
ISSN15710653
Digital Object Identifier (DOI)https://doi.org/10.1016/j.endm.2016.11.002
Web address (URL)http://hdl.handle.net/10545/622413
http://creativecommons.org/licenses/by-nc-sa/4.0/
hdl:10545/622413
Publication datesDec 2016
Publication process dates
Deposited21 Mar 2018, 13:00
SeriesTCDM2016
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Archived with thanks to Electronic Notes in Discrete Mathematics

ContributorsUniversity of Derby and University of Alba Iulia
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Bagdasar, Ovidiu, Hedderwick, Eve and Popa, Ioan-Lucian 2018. On the ratios and geometric boundaries of complex Horadam sequences. Electronic Notes in Discrete Mathematics. https://doi.org/10.1016/j.endm.2018.05.011
ENDM Proceedings for TREPAM'17: Preface
Bagdasar, Ovidiu and Popa, Ioan-Lucian 2018. ENDM Proceedings for TREPAM'17: Preface. Electronic Notes in Discrete Mathematics. https://doi.org/10.1016/j.endm.2018.05.001
Robust generalized Mittag-Leffler synchronization of fractional order neural networks with discontinuous activation and impulses.
Pratap, A., Raja, R., Sowmiya, C., Bagdasar, Ovidiu, Cao, Jinde and Rajchakit, Grienggrai 2018. Robust generalized Mittag-Leffler synchronization of fractional order neural networks with discontinuous activation and impulses. Neural Networks. https://doi.org/10.1016/j.neunet.2018.03.012
Unifying local-global type properties in vector optimization.
Bagdasar, Ovidiu and Popovici, Nicolae 2018. Unifying local-global type properties in vector optimization. Journal of Global Optimization. https://doi.org/10.1007/s10898-018-0656-8
Case studies: Using heuristics.
Lowndes, Val, Bagdasar, Ovidiu and Berry, Stuart 2017. Case studies: Using heuristics. in: Springer.
Further use of heuristic methods.
Lowndes, Val, Berry, Stuart, Parkes, Chris, Bagdasar, Ovidiu and Popovici, Nicolae 2017. Further use of heuristic methods. in: Springer.
New results and conjectures on 2-partitions of multisets.
Bagdasar, Ovidiu and Andrica, Dorin 2017. New results and conjectures on 2-partitions of multisets. Proceedings of the 7th International Conference on Modeling, Simulation, and Applied Optimization (ICMSAO). https://doi.org/10.1109/ICMSAO.2017.7934928
Qualitative case study methodology: Automatic design and correction of ceramic colors
Bagdasar, O., Birluţiu, A., Chen, M. and Popa, I.-L. 2017. Qualitative case study methodology: Automatic design and correction of ceramic colors. IEEE. https://doi.org/10.1109/icstcc.2017.8107118
New results and conjectures on 2-partitions of multisets
Bagdasar, O. and Andrica, D. 2017. New results and conjectures on 2-partitions of multisets. 7th International Conference on Modeling, Simulation, and Applied Optimization, ICMSAO 2017. IEEE Computer Society. https://doi.org/10.1109/icmsao.2017.7934928
ON THE MASKED PERIODICITY OF HORADAM SEQUENCES: A GENERATOR-BASED APPROACH
Bagdasar, Ovidiu D., Larcombe, Peter J. and Bagdasar, O. 2017. ON THE MASKED PERIODICITY OF HORADAM SEQUENCES: A GENERATOR-BASED APPROACH. Fibonacci Quarterly.
LOCAL MAXIMIZERS OF GENERALIZED CONVEX VECTOR-VALUED FUNCTIONS
Bagdasar, Ovidiu, Popovici, Nicolae and Bagdasar, O. 2017. LOCAL MAXIMIZERS OF GENERALIZED CONVEX VECTOR-VALUED FUNCTIONS. Journal of Nonlinear and Convex Analysis.
On the number of complex horadam sequences with a fixed period
Bagdasar, Ovidiu and Larcombe, Peter J. 2013. On the number of complex horadam sequences with a fixed period. Fibonacci Quarterly.
On the characterization of periodic complex Horadam sequences
Bagdasar, Ovidiu and Larcombe, Peter J. 2013. On the characterization of periodic complex Horadam sequences. Fibonacci Quarterly.
On a result of Bunder involving Horadam sequences: A proof and generalization
Larcombe, Peter J. and Bagdasar, Ovidiu 2013. On a result of Bunder involving Horadam sequences: A proof and generalization. Fibonacci Quarterly.
Influence discovery in semantic networks: An initial approach
Trovati, M. and Bagdasar, O. 2014. Influence discovery in semantic networks: An initial approach. IEEE. https://doi.org/10.1109/uksim.2014.48
Complementary iInequalities involving the Stolarsky Mean
Bagdasar, Ovidiu 2010. Complementary iInequalities involving the Stolarsky Mean. Journal of Inequalities and Applications. https://doi.org/10.1155/2010/492570
Concise computer mathematics: tutorials on theory and problems
Bagdasar, Ovidiu 2013. Concise computer mathematics: tutorials on theory and problems. Springer.
On the characterization of periodic generalized Horadam sequences
Bagdasar, Ovidiu and Larcombe, Peter J. 2014. On the characterization of periodic generalized Horadam sequences. Journal of Difference Equations and Applications. https://doi.org/10.1080/10236198.2014.891022
Local maximum points of explicitly quasiconvex functions
Bagdasar, Ovidiu and Popovici, Nicolae 2014. Local maximum points of explicitly quasiconvex functions. Optimization Letters. https://doi.org/10.1007/s11590-014-0781-3
A horadam-based pseudo-random number generator
Bagdasar, O.D., Chen, M. and Bagdasar, O. 2014. A horadam-based pseudo-random number generator. IEEE. https://doi.org/10.1109/uksim.2014.55
On the structure of periodic complex Horadam orbits
Bagdasar, Ovidiu D., Larcombe, Peter J., Anjum, Ashiq and Bagdasar, O. 2016. On the structure of periodic complex Horadam orbits. Carpathian Journal of Mathematics.
Characterizations of Generalized Exponential Trichotomies for Linear Discrete-time Systems
Popa, I.-L., Ceauşu, T., Bagdasar, O. and Agarwal, R.P. 2016. Characterizations of Generalized Exponential Trichotomies for Linear Discrete-time Systems. Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica. 27 (2), pp. 153-166. https://doi.org/10.2478/auom-2019-0025
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
ON A RESULT OF BUNDER INVOLVING HORADAM SEQUENCES: A NEW PROOF
Larcombe, Peter J., Bagdasar, O. and Fennessey, Eric J. 2014. ON A RESULT OF BUNDER INVOLVING HORADAM SEQUENCES: A NEW PROOF. Fibonacci Quarterly. pp. 175-177.