Log-concavity of the Fennessey-Larcombe-French Sequence

2015/03/07 by Yang, Arthur L. B., Zhao, James J. Y.
#05A20 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1503.02151

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.

Related

• Sun's log-concavity conjecture on the Catalan-Larcombe-French sequence
• Log-concavity of Lucas Sequences of first kind
• Log-concavity of rows of Pascal type triangles
• On multiple and infinite log-concavity
• On the combinatorial local log-concavity conjecture and a result of Stanley