<?xml version="1.0" encoding="UTF-8"?>
<article article-type="Research Article">
  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher">journal-of-discrete-mathematical-sciences-and-cryptography</journal-id>
      <journal-title-group>
        <journal-title>Journal of Discrete Mathematical Sciences and Cryptography</journal-title>
      </journal-title-group>
      <issn publication-format="electronic">2169-0065</issn>
      <issn publication-format="print">0972-0529</issn>
      <publisher>
        <publisher-name>Taru Publications</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.47974/JDMSC-1851</article-id>
      <title-group>
        <article-title>A combinatorial interpretation of the Perrin sequence</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Vieira</surname>
            <given-names>Renata P. M.</given-names>
          </name>
          <aff>Postgraduate Program in Education of the Northeast Education Network, (RENOEN), Universidade Federal do Ceará - Campus da UFC, Rua Campus do Pici, Federal University of Ceara, Pici, Fortaleza - CE, Brazil</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Spreafico</surname>
            <given-names>Elen V. P.</given-names>
          </name>
          <aff>Departament of Mathematics, Universidade Federal de Mato Grosso do Sul, Pioneiros, 79070-900, Brazil</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Alves</surname>
            <given-names>Francisco R. V.</given-names>
          </name>
          <aff>Department of Mathematics, Federal Institute of Science and Technology Education of the State of Ceará, Ceara, 60040-531, Brazil</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Catarino</surname>
            <given-names>Paula M. M. C.</given-names>
          </name>
          <aff>Department of Mathematics, University of Trás-os-Montes and Alto Douro, Vila Real, 5001-801, Portugal</aff>
        </contrib>
      </contrib-group>
      <volume>27</volume>
      <issue>8</issue>
      <fpage>2289</fpage>
      <lpage>2300</lpage>
      <pub-date date-type="pub">
        <day>18</day>
        <month>12</month>
        <year>2024</year>
      </pub-date>
      <abstract>
        <p>This study focuses on exploring a combinatorial interpretation for the Perrin sequence, with the goal of making a meaningful contribution to the field of Mathematics education. In view of studies focused on the History of Mathematics containing the teaching of recurring numerical sequences present in textbooks, there is an interest in carrying out a combinatorial approach for a sequence regarded as akin to the Fibonacci numbers, which is the Perrin sequence. In this way, we have the definition of Perrin’s bracelets, investigating Perrin’s combinatorial model. Finally, combinatorial interpretations for the Perrin sequence extensions are discussed, generalizing the Perrin combinatorial model.</p>
      </abstract>
      <kwd-group>
        <kwd>Combinatorics</kwd>
        <kwd>Mathematics teaching</kwd>
        <kwd>Perrin sequence</kwd>
      </kwd-group>
      <custom-meta-group>
        <custom-meta>
          <meta-name>access</meta-name>
          <meta-value>open</meta-value>
        </custom-meta>
        <custom-meta>
          <meta-name>retracted</meta-name>
          <meta-value>no</meta-value>
        </custom-meta>
      </custom-meta-group>
    </article-meta>
  </front>
</article>
