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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 42 Issue: 2

On Generalized Fibonacci And Lucas Numbers By Matrix Methods

Gamaliel Cerda-morales
Pages
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Publication Date
2013-02-01
DOI
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AI Summary & Key Takeaways

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

Using thismatrix representation, we have found some well-known equalities anda Binet-like formula for the generalized Fibonacci and Lucas numbers.

📌 3 Key Takeaways

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Objective & Hypothesis:In this study we define the generalized Lucas V (p, q)-matrix similar tothe generalized Fibonacci U (1, −1)-matrix.
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Key Findings & Data:The V (p, q)-matrix is different from the Fibonacci U (p, q)-matrix, but is related to it.
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Conclusion & Impact:Using thismatrix representation, we have found some well-known equalities anda Binet-like formula for the generalized Fibonacci and Lucas numbers.
🔬Design:Article
📍Scope:Comprehensive Sample
⚙️Variables:Matrix methods · generalized Lucas numbers · Binet’s formula.

Abstract

In this study we define the generalized Lucas V (p, q)-matrix similar tothe generalized Fibonacci U (1, −1)-matrix. The V (p, q)-matrix is different from the Fibonacci U (p, q)-matrix, but is related to it. Using thismatrix representation, we have found some well-known equalities anda Binet-like formula for the generalized Fibonacci and Lucas numbers.

Özet

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Cite This Article

Cerda-morales, G. (2013). On Generalized Fibonacci And Lucas Numbers By Matrix Methods. Hacettepe Journal of Mathematics and Statistics, Volume: 42 Issue: 2. https://ajindex.com/articles/1403487

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References (3)

  1. Gould, H.W.,A history of the Fibonacci Q-matrix and a higher-dimensional problem, Fibonacci Quart. 19, 7-250, 1981.
  2. Horadam, A. F., Jacobsthal representation numbers, Fibonacci Quarterly, 34, 40-54, 1996. Kalman, D. and Mena, R., The Fibonacci numbers - exposed, Math. Mag., 76, 81-167, 2003. Koshy, T.,Fibonacci and Lucas Numbers with Applications, Wiley - Interscience, New York, 200
  3. Silvester, J.R.,Fibonacci properties by matrix methods, Mathematical Gazette 63, 188-191, 197