Research Article
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On Generalized Tribonacci Octonions

Year 2019, Volume: 23 Issue: 5, 731 - 735, 01.10.2019

Arzu Özkoç Öztürk

https://doi.org/10.16984/saufenbilder.525320

Abstract

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.

Keywords

Tribonacci octonion Binet formula tribonacci

References

  • Referans1 O. Keçilioğlu, I. Akkus, ‘The Fibonacci Octonions,’ Advances in Applied Clifford Algebras 25 (2015), 151-158.
  • Referans1 C.C. Yalavigi, ‘Properties of Tribonacci Numbers’, Fibonacci Q. 10(3), 231–246 (1972).
  • Referans3 A.G. Shannon, A.F. Horadam, ‘Some Properties of Third-order Recurrence Relations’, Fibonacci Q. 10(2), 135–146 (1972).
  • Referans4 D. Tascı, ‘Padovan and Pell-Padovan Quaternions’, Journal of Science and Arts, 1(42)2018, 125-132.
  • Referans5 I. Akkus, G. Kizilaslan, ‘On Some Properties of Tribonacci Quaternions’, arXiv:1708.05367, 2017.
  • Referans6 G. Cerda-Morales, ‘Identities for Third Order Jacobsthal Quaternions’, Advances in Applied Clifford Algebras 27(2) (2017), 1043–1053.
  • Referans7 G. Cerda-Morales, ‘The third order Jacobsthal Octonions: Some Combinatorial Properties’, arxiv.org/pdf/1710.00602.pdf.
  • Referans8 C.B. Cimen, A. Ipek, ‘On Jacobsthal and Jacobsthal-Lucas Octonions’, Mediterranean Journal of Mathematics, 14:37 (2017), 1–13.
  • Referans9 A. Ipek, C. Cimen, ‘On (𝑝,𝑞) Fibonacci Octonions’. Mathematica Æterna, 6(6)(2016), 923-932.
  • Referans10 A. Szynal-Liana, I. Włoch, ‘The Pell Quaternions and the Pell Octonions’, Advances in Applied Clifford Algebras 26 (2016), 435–440.
  • Referans11 G. Cerda-Morales, ‘On a Generalization of Tribonacci Quaternions’, Mediterranean Journal of Mathematics 14:239 (2017), 1–12.
  • Referans12 G. Cerda-Morales, ‘The Unifying Formula for all Tribonacci-type Octonions Sequences and Their Properties’, arxiv.org/abs/1807.04140.
  • Referans13 P Catarino, ‘The Modified Pell and Modified k-Pell Quaternions and Octonions’, Advances in Applied Clifford Algebras 26, (2016):577-590.
  • Referans14 A. Karataş, S. Halıcı, ‘Horadam Octonions’, An. S t. Univ. Ovidius Constant A. 25(3)(2017), 97-106.
  • 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.

Year 2019, Volume: 23 Issue: 5, 731 - 735, 01.10.2019

Arzu Özkoç Öztürk

https://doi.org/10.16984/saufenbilder.525320

Abstract

References

  • Referans1 O. Keçilioğlu, I. Akkus, ‘The Fibonacci Octonions,’ Advances in Applied Clifford Algebras 25 (2015), 151-158.
  • Referans1 C.C. Yalavigi, ‘Properties of Tribonacci Numbers’, Fibonacci Q. 10(3), 231–246 (1972).
  • Referans3 A.G. Shannon, A.F. Horadam, ‘Some Properties of Third-order Recurrence Relations’, Fibonacci Q. 10(2), 135–146 (1972).
  • Referans4 D. Tascı, ‘Padovan and Pell-Padovan Quaternions’, Journal of Science and Arts, 1(42)2018, 125-132.
  • Referans5 I. Akkus, G. Kizilaslan, ‘On Some Properties of Tribonacci Quaternions’, arXiv:1708.05367, 2017.
  • Referans6 G. Cerda-Morales, ‘Identities for Third Order Jacobsthal Quaternions’, Advances in Applied Clifford Algebras 27(2) (2017), 1043–1053.
  • Referans7 G. Cerda-Morales, ‘The third order Jacobsthal Octonions: Some Combinatorial Properties’, arxiv.org/pdf/1710.00602.pdf.
  • Referans8 C.B. Cimen, A. Ipek, ‘On Jacobsthal and Jacobsthal-Lucas Octonions’, Mediterranean Journal of Mathematics, 14:37 (2017), 1–13.
  • Referans9 A. Ipek, C. Cimen, ‘On (𝑝,𝑞) Fibonacci Octonions’. Mathematica Æterna, 6(6)(2016), 923-932.
  • Referans10 A. Szynal-Liana, I. Włoch, ‘The Pell Quaternions and the Pell Octonions’, Advances in Applied Clifford Algebras 26 (2016), 435–440.
  • Referans11 G. Cerda-Morales, ‘On a Generalization of Tribonacci Quaternions’, Mediterranean Journal of Mathematics 14:239 (2017), 1–12.
  • Referans12 G. Cerda-Morales, ‘The Unifying Formula for all Tribonacci-type Octonions Sequences and Their Properties’, arxiv.org/abs/1807.04140.
  • Referans13 P Catarino, ‘The Modified Pell and Modified k-Pell Quaternions and Octonions’, Advances in Applied Clifford Algebras 26, (2016):577-590.
  • Referans14 A. Karataş, S. Halıcı, ‘Horadam Octonions’, An. S t. Univ. Ovidius Constant A. 25(3)(2017), 97-106.
  • 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.
There are 15 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Arzu Özkoç Öztürk 0000-0002-2196-3725

Publication Date October 1, 2019
Submission Date February 11, 2019
Acceptance Date March 6, 2019
Published in Issue Year 2019 Volume: 23 Issue: 5

Cite

APA Özkoç Öztürk, A. (2019). On Generalized Tribonacci Octonions. Sakarya University Journal of Science, 23(5), 731-735. https://doi.org/10.16984/saufenbilder.525320
AMA Özkoç Öztürk A. On Generalized Tribonacci Octonions. SAUJS. October 2019;23(5):731-735. doi:10.16984/saufenbilder.525320
Chicago Özkoç Öztürk, Arzu. “On Generalized Tribonacci Octonions”. Sakarya University Journal of Science 23, no. 5 (October 2019): 731-35. https://doi.org/10.16984/saufenbilder.525320.
EndNote Özkoç Öztürk A (October 1, 2019) On Generalized Tribonacci Octonions. Sakarya University Journal of Science 23 5 731–735.
IEEE A. Özkoç Öztürk, “On Generalized Tribonacci Octonions”, SAUJS, vol. 23, no. 5, pp. 731–735, 2019, doi: 10.16984/saufenbilder.525320.
ISNAD Özkoç Öztürk, Arzu. “On Generalized Tribonacci Octonions”. Sakarya University Journal of Science 23/5 (October 2019), 731-735. https://doi.org/10.16984/saufenbilder.525320.
JAMA Özkoç Öztürk A. On Generalized Tribonacci Octonions. SAUJS. 2019;23:731–735.
MLA Özkoç Öztürk, Arzu. “On Generalized Tribonacci Octonions”. Sakarya University Journal of Science, vol. 23, no. 5, 2019, pp. 731-5, doi:10.16984/saufenbilder.525320.
Vancouver Özkoç Öztürk A. On Generalized Tribonacci Octonions. SAUJS. 2019;23(5):731-5.
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