Fibonacci, and Lucas Pascal triangles

Authors : Hacène BELBACHİR, László SZALAY

Pages : 1343-1354

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Publication Date : 2016-10-01

Article Type : Research Paper

Abstract :In this paper, we give explicit formulas for elements of the Fibonacci,  and Lucas Pascal triangles. The structure of these objects and Pascal`s original triangle coincide. Keeping the rule of addition, we replace both legs of the Pascal triangle by the Fibonacci sequence, and the Lucas sequence, respectively. At the end of the study we describe how to determine such a formula for any binary recurrence $\{G_n\}^{\infty}_{n=0}$ satisfying $G_n=G_{n−1}+G_{n−2}$. Other scattered results are also presented.
Keywords : Generalized Pascal`s triangle, Fibonacci sequence, Lucas sequence