KaydedilenlerDerginizi ekleyin

Dergiler / 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
Sayfa
81–87
Yayın Tarihi
2022-07-31
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez: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.
📊
Temel Bulgular & Veri: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.
💡
Sonuç & Katkı:We also present some generalized Fibonacci and Lucas identities using this tiling approach.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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.

🔖

Bu Makaleye Atıf Yap

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

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (14)

  1. A.F. Horadam, A Generalized Fibonacci Sequence, American Mathematical Monthly, Vol. 68, N. 5, pp. 455-459 (1961).
  2. S. Falcon and A. Plaza, On the Fibonacci k-Numbers, Solitons - Fractals. Vol. 32, N. 5, pp. 1615-1624 (2007).
  3. S. Falcon, On the k-Lucas numbers, International Journal of Contemporary Mathematical Sciences, Vol. 6, N. 21, pp. 1039-1050 (2011).
  4. M. El-Mikkawy and T. Sogabe, A New Family of k-Fibonacci Numbers, Applied Mathematics and Computation, Vol. 215, pp.4456–4461 (2010).
  5. Y. Taşyurdu and N. Cobanoğlu and Z. Dilmen, On The A New Family of k-Fibonacci Numbers, Erzincan University Journal of Science and Technology. Vol. 9, N. 1, pp. 95-101 (2016).
  6. Y.K. Panwar, A Note On The Generalized k-Fibonacci Sequence, MTU Journal of Engineering and Natural Sciences, Vol. 2, N. 2, pp. 29-39 (2021).
  7. A. Suvarnamani and M. Tatong, Some Properties of (p, q)-Fibonacci Numbers, Science and Technology RMUTT Journal, Vol. 5, N. 2, pp. 17–21 (2015).
  8. A. Suvarnamani, Some Properties of (p, q)-Lucas Number, Kyungpook Mathematical Journal, Vol. 56, pp. 43-52 (2016).
  9. Y. Taşyurdu, Generalized (p, q)-Fibonacci-Like Sequences and Their Properties, Journal of Mathematics Research, Vol. 11, N. 6, pp. 367-370 (2019).
  10. T.Koshy, Fibonacci and Lucas Numbers with Applications, Wiley, New York USA, (2001).
  11. B.A. Brousseau, Fibonacci Numbers and Geometry, The Fibonacci Quarterly, Vol. 10, N. 3, pp. 303-318 (1972).
  12. R.C. Brigham and R.M. Caron and P.Z. Chinn and R.P. Grimaldi, A Tiling Scheme for the Fibonacci Numbers, J. Recreational Math, Vol. 28, N. 1, pp. 10–17 (1996-97).
  13. A.T. Benjamin and J.J. Quinn, The Fibonacci Numbers Exposed More Discretely, Math. Magazine, Vol. 33, pp. 182–192 (2002).
  14. A.T. Benjamin and J.J. Quinn, Proofs That Really Count The Art of Combinatorial, Proof Mathematical Association of America, (2003).