A TILING APPROACH TO FIBONACCI p-NUMBERS

Year 2022, Volume: 5 Issue: 2, 177 - 184, 31.07.2022

Yasemin Taşyurdu , Berke Cengiz

https://doi.org/10.33773/jum.1142766

Cited By: 2

Abstract

In this paper, we introduce tiling representations of Fibonacci p-numbers, which are generalizations of the well-known Fibonacci and Narayana numbers, and generalized in the distance sense. We obtain Fibonacci p-numbers count the number of distinct ways to tile a 1 × n board using various 1 × r, r-ominoes from r = 1 up to r = p + 1. Moreover, the product identities and sum formulas of these numbers with special subscripts are given by tiling interpretations that allow the derivation of their properties.

Keywords

Fibonacci p-Numbers, Generalized Fibonacci Numbers, Sum Formulas, Tilings

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