A new sequence realizing Lucas numbers, and the Lucas bound
Electronic Journal of Mathematical Analysis and Applications, vol.5, no.1, pp.148-154, 2017 (Peer-Reviewed Journal)
- Publication Type: Article / Article
- Volume: 5 Issue: 1
- Publication Date: 2017
- Journal Name: Electronic Journal of Mathematical Analysis and Applications
- Journal Indexes: zbMATH
- Page Numbers: pp.148-154
- Open Archive Collection: AVESIS Open Access Collection
- Erzincan Binali Yildirim University Affiliated: Yes
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.