On Hybrid Numbers with Gaussian Leonardo Coefficients

Abstract

We consider the Gaussian Leonardo numbers and investigate some of their amazing characteristic properties, including their generating function, the associated Binet formula and Cassini identity, and their matrix representation. Then, we define the hybrid Gaussian Leonardo numbers and obtain some of their particular properties. Furthermore, we define nn Hessenberg matrices whose permanents yield the Leonardo and Gaussian Leonardo sequences.

Keywords

• hybrid Gaussian Leonardo
• generating function
• Binet formula
• Cassini identity
• permanent
• Hessenberg matrix