Log-concavity of the Fennessey-Larcombe-French Sequence

TL;DR

This paper proves the log-concavity of the Fennessey-Larcombe-French sequence using a new sufficient condition related to its three-term recurrence, confirming a recent conjecture by Zhao.

Contribution

It introduces a novel sufficient condition for log-concavity applicable to sequences with three-term recurrence relations, and applies it to prove a specific conjecture.

Findings

Confirmed the log-concavity of the Fennessey-Larcombe-French sequence

Established a new criterion for log-concavity of recurrence-based sequences

Validated Zhao's conjecture on this sequence

Abstract

We prove the log-concavity of the Fennessey-Larcombe-French sequence based on its three-term recurrence relation, which was recently conjectured by Zhao. The key ingredient of our approach is a sufficient condition for log-concavity of a sequence subject to certain three-term recurrence.