A combined approach to Perrin and Padovan hybrid sequences


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Jafari Petroudi S. H. , Pirouz M., Karaca E., YILMAZ F.

Heliyon, vol.7, no.8, 2021 (Peer-Reviewed Journal) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 7 Issue: 8
  • Publication Date: 2021
  • Doi Number: 10.1016/j.heliyon.2021.e07765
  • Journal Name: Heliyon
  • Journal Indexes: Science Citation Index Expanded, Emerging Sources Citation Index, Scopus, CAB Abstracts, Food Science & Technology Abstracts, Veterinary Science Database, Directory of Open Access Journals
  • Keywords: Padovan sequence, Perrin sequence, Hybrid numbers, Generating function

Abstract

© 2021Recently, there has been huge interest to a new numeric set, which brings together three numerical systems: complex, hyperbolic and dual numbers, called as hybrid number. Motivated and based on the importance of this system, we apply the definition of hybrid numbers to Perrin numbers and introduce Perrin hybrid numbers and examine some properties of them. In other words, we obtain their some properties such as Binet-like-formula, partial sums, generating functions, etc. Also we investigate some similar properties with Padovan hybrid sequence. Finally, we give a source Maple 13 code.