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arXiv · 1806.03709

On the third-order Jacobsthal and third-order Jacobsthal-Lucas sequences and their matrix representations

Gamaliel Cerda-Morales
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Abstract

In this paper, we first give new generalizations for third-order Jacobsthal $\{J_{n}^{(3)}\}_{n\in \mathbb{N}}$ and third-order Jacobsthal-Lucas $\{j_{n}^{(3)}\}_{n\in \mathbb{N}}$ sequences for Jacobsthal and Jacobsthal-Lucas numbers. Considering these sequences, we define the matrix sequences which have elements of $\{J_{n}^{(3)}\}_{n\in \mathbb{N}}$ and $\{j_{n}^{(3)}\}_{n\in \mathbb{N}}$. Then we investigate their properties.

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Gamaliel Cerda-Morales. 2018-06-10. On the third-order Jacobsthal and third-order Jacobsthal-Lucas sequences and their matrix representations. https://doi.org/10.1007/s00009-019-1319-9

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