A TILING INTERPRETATION FOR (p,q)-FIBONACCI AND (p,q)-LUCAS NUMBERS

Authors : Yasemin TAŞYURDU, Naime Şeyda TÜRKOĞLU

Pages : 81-87

Doi:10.33773/jum.1142805

View : 20 | Download : 14

Publication Date : 2022-07-31

Article Type : Research Paper

Abstract :In this paper, we introduce a tiling approach to insert ignore into journalissuearticles values(p,q);-Fibonacci and insert ignore into journalissuearticles values(p,q);-Lucas numbers that generalize of the well-known Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal ve Jacobsthal-Lucas numbers. We show that nth insert ignore into journalissuearticles values(p,q);-Fibonacci number is interpreted as the number of ways to tile a 1×n board with cells labeled 1,2,...,n using colored 1×1 squares and 1×2 dominoes, where there are p kind colors for squares and q kind colors for dominoes. Then nth insert ignore into journalissuearticles values(p,q);-Lucas number is interpreted as the number of ways to tile a circular 1×n board with squares and dominoes. We also present some generalized Fibonacci and Lucas identities using this tiling approach.
Keywords : Fibonacci Number, Generalized Fibonacci Numbers, Lucas Number, Tilings