On fourth-order jacobsthal quaternions

Year 2018, Volume: 1 Issue: 2, 73 - 79, 30.09.2018

Gamaliel Cerda-morales

https://doi.org/10.33187/jmsm.434543

Cited By: 2

Abstract

In this paper, we present for the first time a sequence of quaternions of order 4 that we will call the fourth-order Jacobsthal and the fourth-order Jacobsthal-Lucas quaternions. In particular, we are interested in the generating function, Binet formula, explicit formula and some interesting results for fourth-order Jacobsthal quaternions and fourth-order Jacobsthal-Lucas quaternions. This generalizes some previous results given by Szynal-Liana and Wloch in [13], Torunbalci Aydin and Yüce in [14] and Cerda-Morales in [2].

Keywords

Fourth-order Jacobsthal number, Jacobsthal number, quaternion, Recurrence relation

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