A Note on Third-order $k-$Jacobsthal and Third-order $k-$Jacobsthal–Lucas Sequences, and Related Quaternions

Abstract

In this paper, inspired by recent articles of Anatriello and Vincenzi and Morales , we will introduce the third-order $k$-Jacobsthal and third-order $k$-Jacobsthal--Lucas sequences and their associated quaternions. The new results that we have obtained extend most of those obtained in [12].

Keywords

• Recurrence relation
• quaternion
• third-order Jacobsthal number
• third-order Jacobsthal--Lucas number.

References

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