On Fibonacci (k,p)-Numbers and Their Interpretations

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Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi
Volume:27 Issue:2
On Fibonacci (k,p)-Numbers and Their Interpretations

On Fibonacci (k,p)-Numbers and Their Interpretations

Authors : Yasemin TAŞYURDU, Berke CENGİZ

Pages : 235-246

Doi:10.16984/saufenbilder.1173173

View : 97 | Download : 15

Publication Date : 2023-04-30

Article Type : Research Paper

Abstract :In this paper, we define new kinds of Fibonacci numbers, which generalize both Fibonacci, Jacobsthal, Narayana numbers and Fibonacci p-numbers in the distance sense, using the definition of a distance between numbers by a recurrence relation according to a new parameter k. Tiling and combinatorial interpretations of these numbers are presented, and explicit formulas that allow us to calculate the nth number are given. Also, their generating functions are obtained and sums formulas of these numbers with special subscripts are given by tiling interpretations that allow the derivation of their properties.
Keywords : Combinatorial identities, Fibonacci p numbers, generalized Fibonacci numbers, tilings

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