Mathematica Bohemica

Mathematica Bohemica, first online, pp. 1-28

Some identities of Padovan polynomials, Perrin polynomials, Gaussian Padovan, and Gaussian Perrin matrix sequences

Mongkol TATONG

Received April 16, 2025. Published online February 12, 2026.

Abstract: We introduce the recurrence relations of Padovan polynomials, Perrin polynomials, Gaussian Padovan, and Gaussian Perrin matrix sequences, where each matrix consists of elements of polynomials and numbers. For these matrix sequences, we also investigate the $n$th terms, Binet's formulas, generating functions, and summations. Finally, we explore the relationships between these sequences, particularly through their matrix representations, and prove some identities that emerge in this process by matrix algebra.

Keywords: recurrences; matrix sequences; $n$th terms; Binet's formulas

Classification MSC: 11B37, 11C20, 15B36

DOI: 10.21136/MB.2026.0053-25

PDF available at: Institute of Mathematics CAS

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Affiliations: Mongkol Tatong, Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi, Pathum Thani 12110, Thailand, e-mail: mongkol_t@rmutt.ac.th

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