On Hybrid Numbers with Gaussian Leonardo Coefficients

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Kara N., YILMAZ F.

Mathematics, vol.11, no.6, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 6
  • Publication Date: 2023
  • Doi Number: 10.3390/math11061551
  • Journal Name: Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: Binet formula, Cassini identity, generating function, Hessenberg matrix, hybrid Gaussian Leonardo, permanent
  • Open Archive Collection: AVESIS Open Access Collection
  • Ankara Haci Bayram Veli University Affiliated: Yes

Abstract

We consider the Gaussian Leonardo numbers and investigate some of their amazing characteristic properties, including their generating function, the associated Binet formula and Cassini identity, and their matrix representation. Then, we define the hybrid Gaussian Leonardo numbers and obtain some of their particular properties. Furthermore, we define (Formula presented.) Hessenberg matrices whose permanents yield the Leonardo and Gaussian Leonardo sequences.