Log-concavity of Lucas Sequences of first kind

Details Log-concavity of Lucas Sequences of first kind Log-concavity of Lucas Sequences of first kind

2011-01-10

arxiv.org/abs/1101.1805v4

Mathematics

Number Theory

8 pages, no figures, submitted to the Journal of Integers sequences

Scientific paper

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.

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