A combined approach to Perrin and Padovan hybrid sequences

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.