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
Abstract:
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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