RELATIONSHIPS ON MULTIDIMENSIONAL EXTENSIONS OF ONE-ZERO NUMBERS

RELATIONSHIPS ON MULTIDIMENSIONAL EXTENSIONS OF ONE-ZERO NUMBERS

Authors

  • Eudes Antonio Costa Universidade Federal do Tocantins
  • Douglas Catulio Santos
  • Paula Maria Machado Cruz Catarino

DOI:

https://doi.org/10.34179/revisem.v11i1.22618

Abstract

In this paper, we define multidimensional version of One-Zero sequence and look for analogous characterizations with the classic unidimensional sequence. Here, we would like to proceed by analogy with the unidimensional case in order to obtain similar results for bidimensional and k-dimensional for any non-negative integer k. We prove, in particular, results for a bidimensional case, and with mathematical support we extend our study concerning the k-dimensional identities for the One-zero sequence. As a consequence of such properties, we exhibit the Binet Formula associated with k-dimensional identities of this sequence. Furthermore, we exhibit arithmetic properties for the bidimensional sequence, and we study the partial sums of terms in higher dimensions.

Keywords: Binet's Formula; One-Zero sequence; k-dimensional sequence.

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Author Biographies

Eudes Antonio Costa, Universidade Federal do Tocantins

Professor Adjunto da Universidade Federal do Tocantins, Campus Arraias, Colegiado de Matemática. Possui Pós-doutorado em Matemática pela Universidade Federal do Ceará (2019), doutorado em Matemática pela Universidade de Brasília (2013), mestrado em Matemática pela Universidade Federal de Goiás (2001), graduação em Matemática pela Universidade Federal de Goiás (1998) e graduação em Filosofia pela PUC-Goiás (1995). Experiência com Formação de Professores (PROFMAT, Curso de Licenciatura e Cursos de Aperfeiçoamento) e Olimpíadas de Matemática (OBM e OBMEP).

https://orcid.org/0000-0001-6684-9961

Douglas Catulio Santos

Master of Science in Mathematics from the National Professional Master's Program in Mathematics - PROFMAT, held at the Federal University of Tocantins - UFT (2019). Holds a Bachelor's degree in Mathematics from the State University of Bahia - UNEB (2016). Experience as a substitute professor at the Federal University of Tocantins - UFT (2017) and the Federal Institute of Bahia - IFBA (2022-2023).

Paula Maria Machado Cruz Catarino

PAULA CATARINO has a PhD in Mathematics. Full Professor at the Department of Mathematics at the University of Trás-os-Montes and Alto Douro (UTAD). Researcher at the Research Center CMAT-UTAD- CMAT Pole of the University of Minho and also Researcher at the Research Center CIDTFF - Research Center “Didactics and Technology in Trainer Training. Author of several scientific articles published in international peer-reviewed journals.

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Published

2026-04-06

How to Cite

Costa, E. A., Santos, D. C., & Catarino, P. M. M. C. (2026). RELATIONSHIPS ON MULTIDIMENSIONAL EXTENSIONS OF ONE-ZERO NUMBERS. Revista Sergipana De Matemática E Educação Matemática, 11(1), 93–114. https://doi.org/10.34179/revisem.v11i1.22618

Issue

Vol. 11 No. 1 (2026): Revista Sergipana de Matemática e Educação Matemática

Section

Mathematics

License

Copyright (c) 2026 Eudes Antonio Costa, Douglas Catulio Santos, Paula Maria Machado Cruz Catarino

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Creative Commons License

All articles published in this journal are licensed under the Creative Commons Attribution 4.0 International (CC-BY 4.0) license. This means that anyone can copy, distribute, remix, adapt, and use the articles for any purpose, including commercial use, as long as proper attribution is provided to the authors and the journal. For more information about this license, visit: https://creativecommons.org/licenses/by/4.0/