Journal of Integer Sequences, Vol. 13 (2010), Article 10.8.8

Some Properties of Hyperfibonacci and Hyperlucas Numbers

Ning-Ning Cao and Feng-Zhen Zhao
School of Mathematical Sciences
Dalian University of Technology
Dalian 116024


In this paper, we discuss the properties of hyperfibonacci numbers and hyperlucas numbers. We derive some identities for hyperfibonacci and hyperlucas numbers by the method of coefficients. Furthermore, we give asymptotic expansions of certain sums involving hyperfibonacci and hyperlucas numbers by Darboux's method.

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(Concerned with sequences A000048 A000071 A001610 A001924 A023548.)

Received June 6 2010; revised version received September 8 2010. Published in Journal of Integer Sequences, September 10 2010. Corrected, March 26 2011.

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