Log-concavity of Lucas Sequences of first kind
Number Theory
2011-03-08 v4
Abstract
In these notes we address the study of the log-concave operator acting on Lucas Sequences of first kind. We will find for which initial values a generic Lucas sequence is log-concave, and using this we show when the same sequence is infinite log-concave. The main result will help to find the log-concavity of some well known recurrent sequences like Fibonacci and Mersenne. Some possible generalization for a complete classification of the log-concave operator applied to general linear recurrent sequences is proposed.
Keywords
Cite
@article{arxiv.1101.1805,
title = {Log-concavity of Lucas Sequences of first kind},
author = {Piero Giacomelli},
journal= {arXiv preprint arXiv:1101.1805},
year = {2011}
}
Comments
8 pages, no figures, submitted to the Journal of Integers sequences