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            <front>

                <journal-meta>
                                                                <journal-id>saujs</journal-id>
            <journal-title-group>
                                                                                    <journal-title>Sakarya University Journal of Science</journal-title>
            </journal-title-group>
                                        <issn pub-type="epub">2147-835X</issn>
                                                                                            <publisher>
                    <publisher-name>Sakarya University</publisher-name>
                </publisher>
                    </journal-meta>
                <article-meta>
                                        <article-id pub-id-type="doi">10.16984/saufenbilder.525320</article-id>
                                                                <article-categories>
                                            <subj-group  xml:lang="en">
                                                            <subject>Mathematical Sciences</subject>
                                                    </subj-group>
                                            <subj-group  xml:lang="tr">
                                                            <subject>Matematik</subject>
                                                    </subj-group>
                                    </article-categories>
                                                                                                                                                        <title-group>
                                                                                                                        <article-title>On Generalized Tribonacci Octonions</article-title>
                                                                                                                                        </title-group>
            
                                                    <contrib-group content-type="authors">
                                                                        <contrib contrib-type="author">
                                                                    <contrib-id contrib-id-type="orcid">
                                        https://orcid.org/0000-0002-2196-3725</contrib-id>
                                                                <name>
                                    <surname>Özkoç Öztürk</surname>
                                    <given-names>Arzu</given-names>
                                </name>
                                                                    <aff>DUZCE UNIVERSITY</aff>
                                                            </contrib>
                                                                                </contrib-group>
                        
                                        <pub-date pub-type="pub" iso-8601-date="20191001">
                    <day>10</day>
                    <month>01</month>
                    <year>2019</year>
                </pub-date>
                                        <volume>23</volume>
                                        <issue>5</issue>
                                        <fpage>731</fpage>
                                        <lpage>735</lpage>
                        
                        <history>
                                    <date date-type="received" iso-8601-date="20190211">
                        <day>02</day>
                        <month>11</month>
                        <year>2019</year>
                    </date>
                                                    <date date-type="accepted" iso-8601-date="20190306">
                        <day>03</day>
                        <month>06</month>
                        <year>2019</year>
                    </date>
                            </history>
                                        <permissions>
                    <copyright-statement>Copyright © 1997, Sakarya University Journal of Science</copyright-statement>
                    <copyright-year>1997</copyright-year>
                    <copyright-holder>Sakarya University Journal of Science</copyright-holder>
                </permissions>
            
                                                                                                <abstract><p>In this paper, we introduced generalized tribonacci octonion sequence which is a generalization of third order recurrence relations. We investigate many identities which are created by using generalized tribonacci sequence. We get different results for these clases of octonions, comprised recurrence relation, summation formulas, Binet formula, norm value and generating function.</p></abstract>
                                                                                    
            
                                                            <kwd-group>
                                                    <kwd>Tribonacci octonion</kwd>
                                                    <kwd>  Binet formula</kwd>
                                                    <kwd>  tribonacci</kwd>
                                            </kwd-group>
                                                        
                                                                                                                                                    </article-meta>
    </front>
    <back>
                            <ref-list>
                                    <ref id="ref1">
                        <label>1</label>
                        <mixed-citation publication-type="journal">Referans1 O. Keçilioğlu, I. Akkus, ‘The Fibonacci Octonions,’ Advances in Applied Clifford Algebras 25 (2015), 151-158.</mixed-citation>
                    </ref>
                                    <ref id="ref2">
                        <label>2</label>
                        <mixed-citation publication-type="journal">Referans1   C.C. Yalavigi, ‘Properties of Tribonacci Numbers’, Fibonacci Q. 10(3), 231–246 (1972).</mixed-citation>
                    </ref>
                                    <ref id="ref3">
                        <label>3</label>
                        <mixed-citation publication-type="journal">Referans3  A.G. Shannon, A.F. Horadam, ‘Some Properties of Third-order Recurrence Relations’, Fibonacci Q. 10(2), 135–146 (1972).</mixed-citation>
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                        <mixed-citation publication-type="journal">Referans4  D. Tascı, ‘Padovan and Pell-Padovan Quaternions’, Journal of Science and Arts, 1(42)2018, 125-132.</mixed-citation>
                    </ref>
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                        <label>5</label>
                        <mixed-citation publication-type="journal">Referans5  I. Akkus, G. Kizilaslan, ‘On Some Properties of Tribonacci Quaternions’, arXiv:1708.05367, 2017.</mixed-citation>
                    </ref>
                                    <ref id="ref6">
                        <label>6</label>
                        <mixed-citation publication-type="journal">Referans6 G. Cerda-Morales, ‘Identities for Third Order Jacobsthal Quaternions’, Advances in Applied Clifford Algebras 27(2) (2017), 1043–1053.</mixed-citation>
                    </ref>
                                    <ref id="ref7">
                        <label>7</label>
                        <mixed-citation publication-type="journal">Referans7  G. Cerda-Morales, ‘The third order Jacobsthal Octonions: Some Combinatorial Properties’, arxiv.org/pdf/1710.00602.pdf.</mixed-citation>
                    </ref>
                                    <ref id="ref8">
                        <label>8</label>
                        <mixed-citation publication-type="journal">Referans8  C.B. Cimen, A. Ipek, ‘On Jacobsthal and Jacobsthal-Lucas Octonions’, Mediterranean Journal of Mathematics, 14:37 (2017), 1–13.</mixed-citation>
                    </ref>
                                    <ref id="ref9">
                        <label>9</label>
                        <mixed-citation publication-type="journal">Referans9  A. Ipek, C. Cimen, ‘On (𝑝,𝑞) Fibonacci Octonions’. Mathematica Æterna, 6(6)(2016), 923-932.</mixed-citation>
                    </ref>
                                    <ref id="ref10">
                        <label>10</label>
                        <mixed-citation publication-type="journal">Referans10  A. Szynal-Liana, I. Włoch, ‘The Pell Quaternions and the Pell Octonions’, Advances in Applied Clifford Algebras 26 (2016), 435–440.</mixed-citation>
                    </ref>
                                    <ref id="ref11">
                        <label>11</label>
                        <mixed-citation publication-type="journal">Referans11  G. Cerda-Morales, ‘On a Generalization of Tribonacci Quaternions’, Mediterranean Journal of Mathematics 14:239 (2017), 1–12.</mixed-citation>
                    </ref>
                                    <ref id="ref12">
                        <label>12</label>
                        <mixed-citation publication-type="journal">Referans12 G. Cerda-Morales, ‘The Unifying Formula for all Tribonacci-type Octonions Sequences and Their Properties’, arxiv.org/abs/1807.04140.</mixed-citation>
                    </ref>
                                    <ref id="ref13">
                        <label>13</label>
                        <mixed-citation publication-type="journal">Referans13  P Catarino, ‘The Modified Pell and Modified k-Pell Quaternions and Octonions’, Advances in Applied Clifford Algebras 26, (2016):577-590.</mixed-citation>
                    </ref>
                                    <ref id="ref14">
                        <label>14</label>
                        <mixed-citation publication-type="journal">Referans14 A. Karataş, S. Halıcı, ‘Horadam Octonions’, An. S t. Univ. Ovidius Constant A. 25(3)(2017), 97-106.</mixed-citation>
                    </ref>
                                    <ref id="ref15">
                        <label>15</label>
                        <mixed-citation publication-type="journal">Referans15  A. Özkoç Öztürk, A. Porsuk, ‘Some Remarks Regarding the (𝑝,𝑞) -Fibonacci and Lucas Octonion Polynomials’, Universal Journal ofMathematics and Applications, 1 (1) (2018), 46-53.</mixed-citation>
                    </ref>
                            </ref-list>
                    </back>
    </article>
