Abstract This study introduces Fibonacci Cartan and Lucas Cartan numbers, extending the classical Fibonacci and Lucas sequences into the framework of Cartan numbers. By leveraging algebraic and geometric properties, we establish recurrence relations, generating functions, Binet-like formulas, and fundamental identities such as Catalan’s, Cassini’s, and d’Ocagne’s identities for these novel number sequences. Furthermore, summation formulas and additional properties are explored to provide a comprehensive mathematical characterization. The findings contribute to the ongoing development of number theory and its applications in algebra and geometry.
Öztürk et al. (Wed,) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: