A note on generalized Leonardo numbers

By Anthony G. Shannon. Notes on Number Theory and Discrete Mathematics, 2019

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with initial conditions Le0 = Le1 = 1 [2]. The Leonardo number properties are analogues of Fibonacci properties and related to the better known Fibonacci numbers. In that spirit, we extend some of these to generalized Leonardo numbers defined in the spirit of Alwyn Horadam’s generalized Fibonacci sequences {Hn} [3] and {wn} [4]. To do this, we first look at a generalization of {Hn} [5] and then a generalization of {wn} [6]. In both cases, we shall repeat some of their material albeit in slightly different ways and altered notation.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

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