Published: 2022-07-01

On generalized Jacobsthal and Jacobsthal-Lucas numbers

Dorota Bród , Adrian Michalski Logo ORCID

Abstract

Jacobsthal numbers and Jacobsthal–Lucas numbers are some of the most studied special integer sequences related to the Fibonacci numbers. In this study, we introduce one parameter generalizations of Jacobsthal numbers and Jacobsthal–Lucas numbers. We define two sequences, called generalized Jacobsthal sequence and generalized Jacobsthal–Lucas sequence. We give generating functions, Binet’s formulas for these numbers. Moreover, we obtain some identities, among others Catalan’s, Cassini’s identities and summation formulas for the generalized Jacobsthal numbers and the generalized Jacobsthal–Lucas numbers. These properties generalize the well-known results for classical Jacobsthal numbers and Jacobsthal–Lucas numbers. Additionally, we give a matrix representation of the presented numbers.

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Bród, D., & Michalski, A. (2022). On generalized Jacobsthal and Jacobsthal-Lucas numbers. Annales Mathematicae Silesianae, 36(2), 115–128. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13894

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Domyślna okładka

Vol. 36 No. 2 (2022)
Published: 2022-09-30


ISSN: 0860-2107
eISSN: 2391-4238
Ikona DOI 10.1515/amsil

Publisher
University of Silesia Press

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