Summary: In this paper, we discuss the properties of the hyperfibonacci numbers $F\_{n}$^[<r>] and hyperlucas numbers <L>_<n>^[r]. We investigate the log-concavity (log-convexity) of hyperfibonacci numbers and hyperlucas numbers. For example, we prove that ${F\_{n}^$[r]_n ge1 is log-concave. In addition, we also study the log-concavity (log-convexity) of generalized hyperfibonacci numbers and hyperlucas numbers.

log-convexity, log-concavity, Fibonacci number, Lucas number