Journal of Integer Sequences, Vol. 17 (2014), Article 14.1.4

On the Log-Concavity of the Hyperfibonacci Numbers and the Hyperlucas Numbers

Li-Na Zheng and Rui Liu
School of Mathematical Sciences
Dalian University of Technology
Dalian 116024
P. R. China

Feng-Zhen Zhao
Department of Mathematics
Shanghai University
Shanghai 200444
P. R. China


In this paper, we discuss the properties of the hyperfibonacci numbers Fn[r] and hyperlucas numbers Ln[r]. We investigate the log-concavity (log-convexity) of hyperfibonacci numbers and hyperlucas numbers. For example, we prove that {Fn[r]}n ≥ 1 is log-concave. In addition, we also study the log-concavity (log-convexity) of generalized hyperfibonacci numbers and hyperlucas numbers.

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(Concerned with sequences A000071 A001610.)

Received March 17 2013; revised versions received November 9 2013; November 24 2013. Published in Journal of Integer Sequences, December 16 2013.

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