Ordered Leonardo Quadruple Numbers

In this paper, we introduce a new quadruple number sequence by means of Leonardo numbers, which we call ordered Leonardo quadruple numbers. We determine the properties of ordered Leonardo quadruple numbers including relations with Leonardo, Fibonacci, and Lucas numbers. Symmetric and antisymmetric p...

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Bibliographic Details
Published in:Symmetry (Basel) 2023-01, Vol.15 (1), p.149
Main Authors: Nurkan, Semra Kaya, Güven, İlkay Arslan
Format: Article
Language:English
Subjects:
Algebra
Euclidean space
Fibonacci
Fibonacci numbers
Fibonacci quaternions
Identities
Leonardo numbers
Number systems
quadruple numbers
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Summary:In this paper, we introduce a new quadruple number sequence by means of Leonardo numbers, which we call ordered Leonardo quadruple numbers. We determine the properties of ordered Leonardo quadruple numbers including relations with Leonardo, Fibonacci, and Lucas numbers. Symmetric and antisymmetric properties of Fibonacci numbers are used in the proofs. We attain some well-known identities, the Binet formula, and a generating function for these numbers. Finally, we provide illustrations of the identities.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym15010149