Matrix representations of the q-Jacobsthal numbers

Authors

  • Gamaliel Cerda Morales Pontificia Universidad Católica de Valparaiso.

DOI:

https://doi.org/10.4067/S0716-09172012000400003

Keywords:

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.

Author Biography

Gamaliel Cerda Morales, Pontificia Universidad Católica de Valparaiso.

Instituto de Matemáticas.

References

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[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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