On Leonardo Numbers and Fibonacci Fundamental System
摘要
Our goal is to explore the generalized Leonardo numbers, through the properties of the Fibonacci fundamental systems related to the elements of this sequence. We explicitly describe the closed connection between the sequences of the Fibonacci fundamental system and the generalized Leonardo numbers. Moreover, the matrix approach is considered for studying the combinatorial identities and the generalized Cassini identity for the generalized Leonardo numbers. In addition, the analytical aspect about each sequence of the generalized Leonardo numbers is elaborated. Finally, the combinatorial and the analytical formula of the generalized Cassini identity are investigated.