Matrix representations of the q-Jacobsthal numbers
DOI:
https://doi.org/10.4067/S0716-09172012000400003Keywords:
q-Jacobsthal numbers, q-Jacobsthal-Lucas numbers, matrix methods, números de q-Jacobsthal, números de q-Jacobsthal-Lucas, métodos matriciales.Abstract
In this paper, we consider a q-Jacobsthal sequence {Jq,n},with initial conditions Jq0 = 0 and Jq1 = l. Then give a generating matrix for the terms of sequence {Jq,kn} for a positive integer k.With the aid of this matrix, we derive some new identities for the sequence.References
[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. 55-64, (2012).
[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, (2010).
[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, (2008).
[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. Math. Soc., Vol. 15, no. 1, pp. 23-36, (2009).
[Ko] T. Koshy, Fibonacci and Lucas Numbers with Applications, A Wiley Interscience Publications, New York, (2002).
[C2] G. Cerda-Morales, Matrix methods in Horadam Sequences, Boletin de matematicas, Universidad Nacional de Colombia, Vol. 19, no. 1, pp. 55-64, (2012).
[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, (2010).
[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, (2008).
[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. Math. Soc., Vol. 15, no. 1, pp. 23-36, (2009).
[Ko] T. Koshy, Fibonacci and Lucas Numbers with Applications, A Wiley Interscience Publications, New York, (2002).
Published
2013-02-19
How to Cite
[1]
G. Cerda Morales, “Matrix representations of the q-Jacobsthal numbers”, Proyecciones (Antofagasta, On line), vol. 31, no. 4, pp. 345-354, Feb. 2013.
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