# On the masked periodicity of Horadam sequences: A generator-based approach.

Journal article

*Fibonacci Quarterly.*

Authors | Bagdasar, Ovidiu and Larcombe, Peter J. |
---|---|

Abstract | The Horadam sequence is a general second order linear recurrence sequence, dependent on a family of four (possibly complex) parameters|two recurrence coe cients and two initial conditions. In this article we examine a phenomenon identi ed previously and referred to as `masked' periodicity, which links the period of a self-repeating Horadam sequence to its initial conditions. This is presented in the context of cyclicity theory, and then extended to periodic sequences arising from recursion equations of degree three or more. |

The Horadam sequence is a general second order linear recurrence sequence, | |

Keywords | Recurrent sequences; Horadam sequences; Periodicity; Geometric patterns |

Year | 2017 |

Journal | Fibonacci Quarterly |

Publisher | The Fibonacci Association |

ISSN | 00150517 |

Web address (URL) | http://hdl.handle.net/10545/622397 |

http://creativecommons.org/licenses/by-nc-sa/4.0/ | |

hdl:10545/622397 | |

Publication dates | Nov 2017 |

Publication process dates | |

Deposited | 21 Mar 2018, 10:14 |

Contributors | University of Derby |

File | File Access Level Open |

File | File Access Level Open |

File | File Access Level Open |

https://repository.derby.ac.uk/item/94v6v/on-the-masked-periodicity-of-horadam-sequences-a-generator-based-approach

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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).*

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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