Fibonacci, and Lucas Pascal triangles

Year 2016, Volume: 45 Issue: 5, 1343 - 1354, 01.10.2016

Hacène Belbachir , László Szalay

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

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