A new sequence realizing Lucas numbers, and the Lucas bound

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Özkan E., Göçer A. A., Altun İ.

Electronic Journal of Mathematical Analysis and Applications, vol.5, no.1, pp.148-154, 2017 (Peer-Reviewed Journal)

Abstract

We define a set L(n) of vectors with positive integral entries. We show that the cardinality of L(n) is the nth Lucas number Ln, for n ≥ 1. We then show that the number l(n) of M-sequences of length n is bounded by the Lucas number Ln, for n ≥ 1. This is an analog of similar statements with Fibonacci numbers Fn instead of Lucas numbers.