K-Leonardo's hybrid numbers

Abstract

This work presents a study on the hybrid numbers of K-Leonardo, based on the results obtained on the Leonardo sequence presented at first by Catarino and Borges (2020) and on the set of hybrid numbers, initially presented by Özdemir (2018). At first, we will define the K-Leonardo sequence, its recurrence and its initial terms, and also, we will define the set of hybrid numbers and properties inherent to these numbers. Thus, throughout the text we will discuss the hybridization of the K-Leonardo sequence, which consists of associating the set of hybrid numbers to the K-Leonardo sequence. In this way, we will present a new recurrence, its initial terms, its extension to the terms of nonpositive indices, characteristic polynomial, matrix form, generating function, Binet formula and properties linked to K-Leonardo hybrids. This work aims to study and explore the Leonardo sequence and present new mathematical results linked to this sequence.