# 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.*Authors | Bagdasar, 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. |

Keywords | Recurrent sequences; Fibonacci numbers; Periodic sequences |

Year | 2013 |

Journal | Fibonacci Quarterly |

Publisher | Fibonacci Association |

ISSN | 0015-0517 |

Web address (URL) | http://hdl.handle.net/10545/620939 |

http://creativecommons.org/licenses/by/4.0/ | |

hdl:10545/620939 | |

Publication dates | 01 Feb 2013 |

Publication process dates | |

Deposited | 21 Nov 2016, 16:07 |

Contributors | University of Derby |

File | File Access Level Open |

File | File Access Level Open |

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https://repository.derby.ac.uk/item/926y1/on-the-characterization-of-periodic-complex-horadam-sequences

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Larcombe, Peter J. 2014. Closed form evaluations of some series involving Catalan numbers.*Bulletin of the Institute of Combinatorics and its Applications (ICA).*

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Larcombe, Peter J. and Fennessey, Eric J. 2015. A condition for anti-diagonals product invariance across powers of $2 \times 2$ matrix sets characterizing a particular class of polynomial families.*Fibonacci Quarterly.*

##### On the phenomenon of masked periodic Horadam sequences

Larcombe, Peter J. and Fennessey, Eric J. 2015. On the phenomenon of masked periodic Horadam sequences.*Utilitas Mathematica.*

##### On horadam sequence periodicity: A new approach

Larcombe, Peter J. and Fennessey, Eric J. 2015. On horadam sequence periodicity: A new approach.*Bulletin of the Institute of Combinatorics and its Applications (ICA).*

##### A non-linear identity for a particular class of polynomial families

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