Submitted:
19 April 2020
Posted:
19 April 2020
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Abstract
In this paper, inspired by recent articles of G. Anatriello and G. Vincenzi (see \cite{Ana}), and G. Cerda-Morales (see \cite{Cer1,Cer2}), we will introduce the third-order $\overline{h}$-Jacobsthal and third-order $\overline{h}$-Jacobsthal--Lucas sequences and their associated quaternions. The new results that we have obtained extend most of those obtained in \cite{Cer2}.
Keywords:
recurrence relations
; quaternions
; third-order Jacobsthal numbers
; third-order Jacobsthal--Lucas numbers
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