Fikri KÖKEN, Durmuş BOZKURT

148101

On Lucas numbers by the matrix method

On Lucas numbers by the matrix method

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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  • [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).
Hacettepe Journal of Mathematics and Statistics-Cover
  • Yayın Aralığı: 6
  • Başlangıç: 2002
  • Yayıncı: Hacettepe Üniversitesi Fen Fakultesi
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