<?xml version="1.0" encoding="UTF-8"?>
<article article-type="Research Article">
  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher">journal-of-information-and-optimization-sciences</journal-id>
      <journal-title-group>
        <journal-title>Journal of Information and Optimization Sciences</journal-title>
      </journal-title-group>
      <issn publication-format="electronic">2169-0103</issn>
      <issn publication-format="print">0252-2667</issn>
      <publisher>
        <publisher-name>Taru Publications</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.47974/JIOS-1940</article-id>
      <title-group>
        <article-title>More identities on r-Pell and r-Pell hybrid numbers</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Yılmaz</surname>
            <given-names>Nazmiye</given-names>
          </name>
          <aff>Department of Mathematics, Faculty of Kamil Ozdag Science, Karamanoğlu Mehmetbey University, Karaman, 70100, Turkey</aff>
        </contrib>
      </contrib-group>
      <volume>47</volume>
      <issue>4</issue>
      <fpage>1451</fpage>
      <lpage>1460</lpage>
      <pub-date date-type="pub">
        <day>09</day>
        <month>12</month>
        <year>2025</year>
      </pub-date>
      <abstract>
        <p>Regarding r-Pell numbers, we provide some identities. The r-Pell numbers with negative subscripts are shown below. The binomial summations for the r-Pell numbers are obtained. Several identities pertaining to r-Pell hybrid numbers are provided. We provide the negative subscripted r-Pell hybrid numbers. We develop various Cassini identities for the conjugate of the r-Pell hybrid numbers in accordance with two different determinant definitions of a hybrid square matrix (whose entries are hybrid numbers).</p>
      </abstract>
      <kwd-group>
        <kwd>Binomial</kwd>
        <kwd>Pell hybrid number</kwd>
        <kwd>(r</kwd>
        <kwd>n)-Pell number</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>
