## Abstract

Given k ≥ 2, let a_{n} be the sequence defined by the recurrence a_{n} = α_{1}a_{n-1} + ⋯ + α_{k}a_{n-k} for n ≥ k, with initial values a_{0} = a_{1} = ⋯ = a_{k-2} = 0 and a_{k-1} = 1. We show under a couple of assumptions concerning the constants α_{i} that the ratio annan-1n-1 n√an/n-1√an-1 is strictly decreasing for all n ≥ N, for some N depending on the sequence, and has limit 1. In particular, this holds in the cases when all of the α_{i} are unity or when all of the α_{i} are zero except for the first and last, which are unity. Furthermore, when k = 3 or k = 4, it is shown that one may take N to be an integer less than 12 in each of these cases.

Original language | English |
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Pages (from-to) | 585-592 |

Number of pages | 8 |

Journal | Mathematica Slovaca |

Volume | 67 |

Issue number | 3 |

DOIs | |

State | Published - 27 Jun 2017 |

### Bibliographical note

Publisher Copyright:© 2017 Mathematical Institute Slovak Academy of Sciences 2017.

## Keywords

- k-Fibonacci numbers
- log-concavity
- monotonicity

## ASJC Scopus subject areas

- General Mathematics