A TILING APPROACH TO FIBONACCI p-NUMBERS
Authors : Yasemin Taşyurdu, Berke Cengiz
Pages : 177-184
Doi:10.33773/jum.1142766
View : 19 | Download : 6
Publication Date : 2022-07-31
Article Type : Research
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