On Jacobsthal–Narayana and Jacobsthal-Narayana-Lucas Sequences

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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