Some Tridiagonal Matrix of the Repunit Sequence

Eudes Antonio Costa; Douglas Catulio dos Santos; Paula Maria Machado Cruz Catarino

doi:10.14244/lajm.v4i1.33

Authors

Eudes Antonio Costa Federal University of Tocantins https://orcid.org/0000-0001-6684-9961
Douglas Catulio dos Santos Education Department of the State of Bahia https://orcid.org/0000-0002-5221-6087
Paula Maria Machado Cruz Catarino University of Trás-os-Montes and Alto Douro https://orcid.org/0000-0001-6917-5093

DOI:

https://doi.org/10.14244/lajm.v4i1.33

Keywords:

Horadam sequence, Repunit sequence, Tridiagonal matrices

Abstract

This paper explores the connection between tridiagonal matrices and the repunit sequence, which is a type of Horadam sequence, and aims to establish new representations of repunit sequences using distinct tridiagonal matrices and their determinants. Motivated by earlier work relating tridiagonal matrices to second-order linear recurrences, we present another representation of the repunit sequence by tridiagonal matrices.

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