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

Year 2023, Volume: 27 Issue: 2, 235 - 246, 30.04.2023

Yasemin TAŞYURDU Berke CENGİZ

https://doi.org/10.16984/saufenbilder.1173173

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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