Matrix representations of the q-Jacobsthal numbers

• Cerda Morales, Gamaliel ^[1]
  1. [1] Pontificia Universidad Católica de Valparaíso

     Pontificia Universidad Católica de Valparaíso

     Valparaíso, Chile

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 31, Nº. 4, 2012, págs. 345-354
• Idioma: inglés
• DOI: 10.4067/S0716-09172012000400003
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we consider a q-Jacobsthal sequence {Jq¡n},with initial conditions Jq0 = 0 and Jq! = l. Then give a generating matrix for the terms of sequence {Jq־fen| for a positive integer k.With the aid of this matrix, we derive some new identities for the sequence

• Referencias bibliográficas
  • Citas [C1] G. Cerda-Morales, On generalized Fibonacci and Lucas numbers by matrix methods, Hacettepe J. Math. Stat. (to appear).
  • [C2] G. Cerda-Morales, Matrix methods in Horadam Sequences, Boletin de matematicas, Universidad Nacional de Colombia, Vol. 19, no. 1, pp....
  • [H1] A.F. Horadam, Basic properties of a certain generalized sequence of numbers, Fibonacci Quarterly, Vol. 3, pp. 161-176, (1965).
  • [H2] A. F. Horadam, Jacobsthal Representation Numbers, The Fibonacci Quarterly, Vol. 34, no. 1, pp. 40-53, (1996).
  • [KB1] F. Koken, D. Bozkurt, On Lucas numbers by the matrix method, Hacettepe Journal of Mathematics and Statistics, Vol. 39, no. 4, pp. 471-475,...
  • [KB2] F. Koken, D. Bozkurt, On The Jacobsthal numbers by matrix methods, Int. J. Contemp. Math. Sciences, Vol. 3, no. 13, pp. 605-614, (2008).
  • [KB3] F. Koken, D. Bozkurt, On The Jacobsthal-Lucas Numbers by Matrix Methods, Int. J. Contemp. Math. Sciences, Vol. 3, no. 33, pp. 1629-1633,...
  • [KM] D. Kalman, R. Mena, The Fibonacci numbers- exposed, Math. Mag., no. 76, pp. 81-167, 2003.
  • [KS] E. Kilic, P. Stanica, Factorizations and representations of second linear recurrences with indices in arithmetic progressions, Bol. Mex....
  • [Ko] T. Koshy, Fibonacci and Lucas Numbers with Applications, A Wiley Interscience Publications, New York, (2002).