On the generating matrices of thee Κ-Fibonacci numbers

• Falcon, Sergio ^[1]
  1. [1] Universidad de Las Palmas de Gran Canaria

     Universidad de Las Palmas de Gran Canaria

     Gran Canaria, España

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 32, Nº. 4, 2013, págs. 347-357
• Idioma: inglés
• DOI: 10.4067/S0716-09172013000400004
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• Resumen

  • In this paper we define some tridiagonal matrices depending of a parameter from which we will find the k-Fibonacci numbers. And from the cofactor matrix of one of these matrices we will prove some formulas for the k-Fibonacci numbers differently to the traditional form. Finally, we will study the eigenvalues of these tridiagonal matrices.

• Referencias bibliográficas
  • Citas [1] Falcon S. and Plaza A., On the Fibonacci k-numbers, Chaos, Solit. & Fract. 32 (5), pp. 1615—1624, (2007).
  • [2] Falcon S. and Plaza A., The k-Fibonacci sequence and the Pascal 2-triangle, Chaos, Solit. & Fract. 33 (1), pp. 38—49, (2007).
  • [3] Falcon S. and Plaza A., The k-Fibonacci hyperbolic functions, Chaos, Solit. & Fract. 38 (2), pp. 409—420, (2008).
  • [4] Feng A., Fibonacci identities via determinant of tridiagonal matrix, Applied Mathematics and Computation, 217, pp. 5978—5981, (2011).
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  • [6] Hoggat V. E. Fibonacci and Lucas numbers, Houghton—Miffin, (1969).
  • [7] Horadam A. F. A generalized Fibonacci sequence, Mathematics Magazine, 68, pp. 455—459, (1961).
  • [8] Usmani R., Inversion of a tridiagonal Jacobi matrix, Linear Algebra Appl. 212/213, pp. 413—414, (1994). [9] Wikipedia, http://en.wikipedia.org/wiki/Cofactor...