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Padovan and Pell-Padovan Octonions

Year 2019, Volume: 11, 114 - 122, 30.12.2019

Abstract

In this paper, we define the Padovan and Pell-Padovan octonions by using the Padovan and Pell-Padovan numbers. We give the generating functions, Binet's
formulas, sums formulas and some properties for these octonions. We also present the matrix representations of the Padovan and Pell-Padovan octonions.

References

  • Akkus, I., Ke\c{c}ilioglu, O., \textit{Split Fibonacci and Lucas octonions}, Adv. Appl. Clifford Algebras, \textbf{25(3)}(2015), 517--525.
  • Baez, J., \textit{The octonions}, Bull. Amer. Math. Soc., \textbf{39(2)}(2002), 145--205.
  • Catarino, P., \textit{The modified Pell and the modified $k$-Pell quaternions and octonions}, Adv. Appl. Clifford Algebras, \textbf{26}(2016), 577--590.
  • Cerda-Morales, G., \textit{On a generalization of Tribonacci Quaternions}, Mediterr. J. Math., \textbf{14:239}(2017), 1--12.
  • Cimen, C.B., \.{I}pek, A., \textit{On Pell quaternions and Pell--Lucas quaternions}, Adv. Appl. Clifford Algebras, \textbf{26(1)}(2016), 39--51.
  • Cimen, C.B., \.{I}pek, A., \textit{On Jacobsthal and Jacobsthal--Lucas octonions}, Mediterr. J. Math., \textbf{14(37)}(2017), 13p.
  • Culbert, C., \textit{Cayley-Dickson algebras and loops}, Journal of Generalized Lie Theory and Applications, \textbf{1(1)}(2007), 1--17.
  • Horadam, A.F., \textit{Complex Fibonacci numbers and Fibonacci quaternions}, Am. Math. Month., \textbf{70}(1963), 289--291.
  • Ke\c{c}ilio\u{g}lu, O., Akku\c{s}, I., \textit{The Fibonacci Octonions}, Adv. Appl. Clifford Algebra, \textbf{25}(2015), 151--158.
  • Kritsana, S., \textit{Matrices formula for Padovan and Perrin sequences}, Applied Mathematics Science, \textbf{7(142)}(2013), 7093--7096.
  • Koshy, T., Fibonacci and Lucas Numbers with Applications, Wiley-Interscience, New York, 2001.
  • Koshy, T., \textit{Fibonacci, Lucas and Pell numbers and Pascal's triangle}, Math. Spectrum, \textbf{43}(2011), 125--132.
  • Ser\^{o}dio, R., \textit{On octonionic polynomials}, Adv. Appl. Clifford Algebras, \textbf{17(2)}(2007), 245--258.
  • Tian, Y., \textit{Matrix representations of octonions and their applications}, Adv. Appl. Clifford Algebras, \textbf{10(1)}(2000), 61--90.
Year 2019, Volume: 11, 114 - 122, 30.12.2019

Abstract

References

  • Akkus, I., Ke\c{c}ilioglu, O., \textit{Split Fibonacci and Lucas octonions}, Adv. Appl. Clifford Algebras, \textbf{25(3)}(2015), 517--525.
  • Baez, J., \textit{The octonions}, Bull. Amer. Math. Soc., \textbf{39(2)}(2002), 145--205.
  • Catarino, P., \textit{The modified Pell and the modified $k$-Pell quaternions and octonions}, Adv. Appl. Clifford Algebras, \textbf{26}(2016), 577--590.
  • Cerda-Morales, G., \textit{On a generalization of Tribonacci Quaternions}, Mediterr. J. Math., \textbf{14:239}(2017), 1--12.
  • Cimen, C.B., \.{I}pek, A., \textit{On Pell quaternions and Pell--Lucas quaternions}, Adv. Appl. Clifford Algebras, \textbf{26(1)}(2016), 39--51.
  • Cimen, C.B., \.{I}pek, A., \textit{On Jacobsthal and Jacobsthal--Lucas octonions}, Mediterr. J. Math., \textbf{14(37)}(2017), 13p.
  • Culbert, C., \textit{Cayley-Dickson algebras and loops}, Journal of Generalized Lie Theory and Applications, \textbf{1(1)}(2007), 1--17.
  • Horadam, A.F., \textit{Complex Fibonacci numbers and Fibonacci quaternions}, Am. Math. Month., \textbf{70}(1963), 289--291.
  • Ke\c{c}ilio\u{g}lu, O., Akku\c{s}, I., \textit{The Fibonacci Octonions}, Adv. Appl. Clifford Algebra, \textbf{25}(2015), 151--158.
  • Kritsana, S., \textit{Matrices formula for Padovan and Perrin sequences}, Applied Mathematics Science, \textbf{7(142)}(2013), 7093--7096.
  • Koshy, T., Fibonacci and Lucas Numbers with Applications, Wiley-Interscience, New York, 2001.
  • Koshy, T., \textit{Fibonacci, Lucas and Pell numbers and Pascal's triangle}, Math. Spectrum, \textbf{43}(2011), 125--132.
  • Ser\^{o}dio, R., \textit{On octonionic polynomials}, Adv. Appl. Clifford Algebras, \textbf{17(2)}(2007), 245--258.
  • Tian, Y., \textit{Matrix representations of octonions and their applications}, Adv. Appl. Clifford Algebras, \textbf{10(1)}(2000), 61--90.
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Yasemin Taşyurdu 0000-0002-9011-8269

Ayşe Akpınar

Publication Date December 30, 2019
Published in Issue Year 2019 Volume: 11

Cite

APA Taşyurdu, Y., & Akpınar, A. (2019). Padovan and Pell-Padovan Octonions. Turkish Journal of Mathematics and Computer Science, 11, 114-122.
AMA Taşyurdu Y, Akpınar A. Padovan and Pell-Padovan Octonions. TJMCS. December 2019;11:114-122.
Chicago Taşyurdu, Yasemin, and Ayşe Akpınar. “Padovan and Pell-Padovan Octonions”. Turkish Journal of Mathematics and Computer Science 11, December (December 2019): 114-22.
EndNote Taşyurdu Y, Akpınar A (December 1, 2019) Padovan and Pell-Padovan Octonions. Turkish Journal of Mathematics and Computer Science 11 114–122.
IEEE Y. Taşyurdu and A. Akpınar, “Padovan and Pell-Padovan Octonions”, TJMCS, vol. 11, pp. 114–122, 2019.
ISNAD Taşyurdu, Yasemin - Akpınar, Ayşe. “Padovan and Pell-Padovan Octonions”. Turkish Journal of Mathematics and Computer Science 11 (December 2019), 114-122.
JAMA Taşyurdu Y, Akpınar A. Padovan and Pell-Padovan Octonions. TJMCS. 2019;11:114–122.
MLA Taşyurdu, Yasemin and Ayşe Akpınar. “Padovan and Pell-Padovan Octonions”. Turkish Journal of Mathematics and Computer Science, vol. 11, 2019, pp. 114-22.
Vancouver Taşyurdu Y, Akpınar A. Padovan and Pell-Padovan Octonions. TJMCS. 2019;11:114-22.