Two Generalizations of Dual-Hyperbolic Balancing Numbers

Abstract

In this paper, we study two generalizations of dual-hyperbolic balancing numbers: dual-hyperbolic Horadam numbers and dual-hyperbolic k-balancing numbers. We give Catalan’s identity, Cassini’s identity, and d’Ocagne’s identity for them.

Keywords

• balancing numbers
• Diophantine equation
• dual-hyperbolic numbers
• Binet formula
• Catalan’s identity