A note on modified third-order Jacobsthal numbers

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-2020-02-0025

Keywords:

Recurrence relation

Abstract

Modified third-order Jacobsthal sequence is defined in this study. Some properties involving this sequence, including the Binet-style formula and the generating function are also presented.

Author Biography

Gamaliel Cerda-Morales, Pontificia Universidad Católica de Valparaíso.

Instituto de Matemáticas.

References

P. Barry, “Triangle geometry and Jacobsthal numbers”, Bulletin - Irish Mathematical Society, 51, pp. 45-57, 2003. [On line]. Available: https://bit.ly/2SaAWbl

G. Cerda-Morales, “Identities for third order Jacobsthal quaternions”, Advances in applied clifford algebras, vol. 27, no. 2, pp. 1043–1053, Mar. 2016, doi: 10.1007/s00006-016-0654-1.

G. Cerda-Morales, “On a generalization for Tribonacci Qquaternions”, Mediterranean journal of mathematics, vol. 14, no. 6, art. ID. 239, Nov. 2017. doi: 10.1007/s00009-017-1042-3.

G. Cerda-Morales, “Dual third-order Jacobsthal quaternions”, Proyecciones (Antofagasta. On line), vol. 37, no. 4, pp. 731–747, Nov. 2018, doi: 10.4067/S0716-09172018000400731

C. K. Cook and M. R. Bacon, “Some identities for Jacobsthal and Jacobsthal-Lucas numbers satisfying higher order recurrence relations”, Annales mathematicae et informaticae, vol. 41, pp. 27-39, 2013. [On line]. Available: https://bit.ly/2W2XOuK

A. F. Horadam, “Jacobsthal and Pell curves”, The Fibonacci quarterly, vol. 26, no. 1, pp. 79-83, 1988. [On line]. Available: https://bit.ly/2YitKxI

A. F. Horadam, “Jacobsthal representation numbers”, The Fibonacci quarterly, vol. 43, no. 1, pp. 40-54, 1996. [On line].Available: https://bit.ly/3eWwoz8

Published

2020-04-28

How to Cite

[1]
G. Cerda-Morales, “A note on modified third-order Jacobsthal numbers”, Proyecciones (Antofagasta, On line), vol. 39, no. 2, pp. 409-420, Apr. 2020.

Issue

Section

Artículos