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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2010 / Cilt: 39 - Sayı: 4

On Lucas numbers by the matrix method

Fikri KÖKEN
Durmuş BOZKURT
Sayfa
471–475
Yayın Tarihi
2022-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Using this matrix representation, we have found some well-known equalities and a Binet-like formula for the Lucas numbers.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this study we define the Lucas $Q_L$-matrix similar to the Fibonacci Q-matrix.
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Temel Bulgular & Veri:The Lucas $Q_L$-matrix is different from the Fibonacci Q- matrix, but is related to it.
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Sonuç & Katkı:Using this matrix representation, we have found some well-known equalities and a Binet-like formula for the Lucas numbers.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

In this study we define the Lucas $Q_L$-matrix similar to the Fibonacci Q-matrix. The Lucas $Q_L$-matrix is different from the Fibonacci Q- matrix, but is related to it. Using this matrix representation, we have found some well-known equalities and a Binet-like formula for the Lucas numbers.

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Bu Makaleye Atıf Yap

KÖKEN, F., BOZKURT, D. (2022). On Lucas numbers by the matrix method. Hacettepe Journal of Mathematics and Statistics, Cilt: 39 - Sayı: 4, 471–475. https://ajindex.com/articles/530612

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Kaynakça (5)

  1. Gould, H.W. A history of the Fibonacci Q-matrix and a higher-dimensional problem, Fibonacci Quart. 19, 7–250, 1981
  2. Kalman, D. and Mena, R. The Fibonacci numbers – exposed, Math. Mag. 76, 81–167, 2003
  3. Koshy, T. Fibonacci and Lucas Numbers with Applications (Wiley - Interscience, New York, 2001)
  4. Silvester, J.R. Fibonacci properties by matrix methods, Mathematical Gazette 63, 188–191, 1979
  5. Vajda, S. Fibonacci and Lucas numbers, and the Golden Section. Theory and applications (Ellis Horwood Limited, Chichester, 1989).