Some Properties of the Generalized Leonardo Numbers

Abstract

In this study, various properties of the generalized Leonardo numbers, which are one of the generalizations of Leonardo numbers, have been investigated. Additionally, some identities among the generalized Leonardo numbers have been obtained. Furthermore, some identities between Fibonacci numbers and generalized Leonardo numbers have been provided. In the last part of the study, binomial sums of generalized Leonardo numbers have been derived. The results obtained for generalized Leonardo numbers are reduced to Leonardo numbers.