<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Recently, Bród introduced a new Jacobsthal-type sequence which is called <italic>r</italic>-Jacobsthal sequence in current study. After defining the appropriate <italic>r</italic>-Jacobsthal–Lucas sequence for the <italic>r</italic>-Jacobsthal sequence, we obtain some properties of these two sequences. For simpler results, we define two new sequences and examine their properties, too. Finally, we generalize some well-known identities.</p>
</abstract>

Recently, Bród introduced a new Jacobsthal-type sequence which is called r-Jacobsthal sequence in current study. After defining the appropriate r-Jacobsthal–Lucas sequence for the r-Jacobsthal sequence, we obtain some properties of these two sequences. For simpler results, we define two new sequences and examine their properties, too. Finally, we generalize some well-known identities.

On <italic>r</italic>-Jacobsthal and <italic>r</italic>-Jacobsthal-Lucas Numbers

Department of Discrete Mathematics, Faculty of Mathematics and Applied Physics

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution 4.0 International License.

On -Jacobsthal and -Jacobsthal-Lucas Numbers

Recently, Bród introduced a new Jacobsthal-type sequence which is called r-Jacobsthal sequence in current study. After defining the appropriate...

On r-Jacobsthal and r-Jacobsthal-Lucas Numbers

Published Online: Feb 07, 2023

Page range: 16 - 31

Received: Mar 07, 2022

Accepted: Jan 05, 2023

DOI: https://doi.org/10.2478/amsil-2023-0001

Keywords
-Jacobsthal numbers, -Jacobsthal–Lucas numbers, Binet formula

© 2023 Göksal Bilgici et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

On r-Jacobsthal and r-Jacobsthal-Lucas Numbers

Published Online: Feb 07, 2023

Page range: 16 - 31

Received: Mar 07, 2022

Accepted: Jan 05, 2023

DOI: https://doi.org/10.2478/amsil-2023-0001

Keywords-Jacobsthal numbers, -Jacobsthal–Lucas numbers, Binet formula

© 2023 Göksal Bilgici et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
-Jacobsthal numbers, -Jacobsthal–Lucas numbers, Binet formula