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Journals / Journal of Universal Mathematics / 2022 / Cilt: 5 Sayı: 2

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

Yasemin Taşyurdu(Erzincan Binali Yıldırım Üniversitesi)0000-0002-9011-8269
Naime Şeyda Türkoğlu(ERZINCAN BINALI YILDIRIM UNIVERSITY)0000-0003-2301-3958
Pages
81–87
Publication Date
2022-07-31
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We also present some generalized Fibonacci and Lucas identities using this tiling approach.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper, we introduce a tiling approach to (p,q)-Fibonacci and (p,q)-Lucas numbers that generalize of the well-known Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal ve Jacobsthal-Lucas numbers.
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Key Findings & Data:We show that nth (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.
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Conclusion & Impact:We also present some generalized Fibonacci and Lucas identities using this tiling approach.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Fibonacci Number · Generalized Fibonacci Numbers · Lucas Number

Abstract

In this paper, we introduce a tiling approach to (p,q)-Fibonacci and (p,q)-Lucas numbers that generalize of the well-known Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal ve Jacobsthal-Lucas numbers. We show that nth (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 (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.

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Cite This Article

Taşyurdu, Y., Türkoğlu, N. Ş. (2022). A TILING INTERPRETATION FOR (p,q)-FIBONACCI AND (p,q)-LUCAS NUMBERS. Journal of Universal Mathematics, Cilt: 5 Sayı: 2, 81–87. https://doi.org/10.33773/jum.1142805

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