A combined approach to Perrin and Padovan hybrid sequences

Seyyed H Jafari Petroudi; Maryam Pirouz; Emel Karaca; Fatih Yılmaz

doi:10.1016/j.heliyon.2021.e07765

A combined approach to Perrin and Padovan hybrid sequences

Heliyon. 2021 Aug 14;7(8):e07765. doi: 10.1016/j.heliyon.2021.e07765. eCollection 2021 Aug.

Authors

Seyyed H Jafari Petroudi¹, Maryam Pirouz², Emel Karaca³, Fatih Yılmaz³

Affiliations

¹ Department of Mathematics, Payame Noor University, Tehran, Iran.
² Department of Mathematics, Guilan University, Rasht, Iran.
³ Department of Mathematics, Ankara Hacı Bayram Veli University, Turkey.

Abstract

Recently, 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.

Keywords: Generating function; Hybrid numbers; Padovan sequence; Perrin sequence.