A TILING APPROACH TO FIBONACCI p-NUMBERS

Authors : Yasemin TAŞYURDU, Berke CENGİZ
Pages : 177-184
Doi:10.33773/jum.1142766
View : 19 | Download : 12
Publication Date : 2022-07-31
Article Type : Research Paper
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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