On Jacobsthal–Narayana and Jacobsthal-Narayana-Lucas Sequences

Year 2024, Volume: 12 Issue: 1, 55 - 61, 30.04.2024

Seyyed Hossein Jafari Petroudi , Ahmet Daşdemir , Maryam Pirouz

Abstract

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.

Keywords

Binet formula, Circulant matrix, Jacobsthal–Narayana sequence, Third-order sequence, Vajda identity

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