Leonardo cartan numbers and related fibonacci–lucas structures

Abstract

This paper investigates the Leonardo Cartan numbers, defined as an extension of the classical Leonardo sequence through additional algebraic structures. The recurrence relations of these numbers are established, and various summation formulas are derived. Furthermore, key mathematical identities, including Catalan’s and Cassini’s identities, are obtained within the framework of Leonardo Cartan numbers. The relationships among Fibonacci, Lucas, and Leonardo sequences are also explored, thereby highlighting their interconnections. By employing Binet’s formula, several fundamental properties of Leonardo Cartan numbers are confirmed, contributing to a deeper understanding of their algebraic structure.