konuralp j. math. Konuralp Journal of Mathematics 2147-625X Mehmet Zeki SARIKAYA Mathematical Sciences Matematik On Jacobsthal–Narayana and Jacobsthal-Narayana-Lucas Sequences https://orcid.org/0000-0003-4127-9215 Jafari Petroudi Seyyed Hossein Payame Noor University https://orcid.org/0000-0001-8352-2020 Daşdemir Ahmet kastamonu üniversitesi Pirouz Maryam Guilan University 04 30 2024 12 1 55 61 12 06 2022 10 23 2023 Copyright © 2013, Konuralp Journal of Mathematics 2013 Konuralp Journal of Mathematics

This paper introduces two new integer sequences that are the third-order recurrence relations. These are called Jacobsthal–Narayana and Jacobsthal-Lucas-Narayana sequences. In particular, great attention is focused on the identification of the Binet type representations for our new sequence, including the generating functions, some important identities, and generating matrix. Finally, we consider the circulant matrix whose entries are Jacobsthal–Narayana sequence and present an appropriate formula to find eigenvalues of that matrix.

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