Leonardo and hyper-Leonardo numbers via Riordan arrays

Abstract

UDC 511 A generalization of the Leonardo numbers is defined and called the hyper-Leonardo numbers. Infinite lower triangular matrices, whose elements are Leonardo and hyper-Leonardo numbers are considered. Then the A - and Z -sequences of these matrices are obtained. Finally, the combinatorial identities between the hyper-Leonardo and Fibonacci numbers are obtained using the fundamental theorem of the Riordan arrays.