Ordered Leonardo Quadruple Numbers

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Nurkan S. K., Güven İ. A.

Symmetry, vol.15, no.1, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 1
  • Publication Date: 2023
  • Doi Number: 10.3390/sym15010149
  • Journal Name: Symmetry
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: Fibonacci quaternions, Leonardo numbers, quadruple numbers
  • Uşak University Affiliated: Yes

Abstract

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.