On Leonardo Numbers and Fibonacci Fundamental System

This chapter delves into the fascinating world of generalized Leonardo numbers, a sequence closely related to the well-known Fibonacci numbers. By leveraging the Fibonacci fundamental system, the authors explore the combinatorial and analytical aspects of these numbers, establishing new properties and identities. The study includes the exploration of the Casoratian matrix and the derivation of the generalized Cassini identity, providing a deeper understanding of these sequences and their applications in various mathematical contexts. The chapter also presents analytical formulas for the generalized Leonardo numbers, highlighting the significance of these sequences in both theoretical and practical aspects of mathematics and computer science.