Bicomplex Tetranacci and Tetranacci-Lucas Quaternions

Authors

  • Yüksel Soykan Department of Mathematics, Art and Science Faculty, Zonguldak Bülent Ecevit University, 67100, Zonguldak

DOI:

https://doi.org/10.26713/cma.v11i1.1212

Keywords:

Bicomplex Tetranacci numbers, Bicomplex quaternions, Bicomplex Tetranacci quaternions, Bicomplex Tetranacci-Lucas quaternions

Abstract

In this paper, we introduce the bicomplex Tetranacci and Tetranacci-Lucas quaternions. Moreover, we present Binet's formulas, generating functions, and the summation formulas for those bicomplex quaternions.

Downloads

Download data is not yet available.

References

F. T. Aydın, Bicomplex k-Fibonacci quaternions, arXiv 1810.05003 [math.NT] (2018), https: //arxiv.org/abs/1810.05003.

F. T. Aydın, On bicomplex Pell and Pell-Lucas numbers, Communications in Advanced Mathematical Sciences 1(2) (2018), 142 – 155, DOI: 10.33434/cams.439752.

J. Baez, The octonions, Bull. Amer. Math. Soc. 39(2) (2002), 145 – 205, DOI: 10.1090/S0273-0979-01-00934-X.

P. Catarino, Bicomplex k-Pell quaternions, Computational Methods and Function Theory 19(1)(2018), 65 – 76, DOI: 10.1007/s40315-018-0251-5.

G. Cerda, Bicomplex third-order Jacobsthal quaternions, arXiv 1809.06979 [math.AC] (2018), https://arxiv.org/abs/1809.06979.

J. H. Conway and D. A. Smith, On Quaternions and Octonions: Their Geometry, Arithmetic and Symmetry, A. K. Peters/CRC Press (2003), DOI: 10.1017/S002555720017545X.

G. P. Dresden and Z. Du, A simplified Binet formula for k-generalized Fibonacci numbers, Journal of Integer Sequences 17 (2014), article 14.4.7, pages 9, https://cs.uwaterloo.ca/journals/JIS/VOL17/Dresden/dresden6.pdf.

S. Halıcı and A. Karatas, Bicomplex Lucas and Horadam numbers, arXiv 1806.05038v2 [math.RA] (2018), https://arxiv.org/abs/1806.05038.

S. Halici, On bicomplex Fibonacci numbers and their generalization, in Models and Theories in Social Systems. Studies in Systems, Decision and Control, C. Flaut, Å . Hošková-Mayerová and D. Flaut (eds.), Vol. 179, 509 – 524, Springer (2019), DOI: 10.1007/978-3-030-00084-4_26.

G. S. Hathiwala and D. V. Shah, Binet-type formula for the sequence of Tetranacci numbers by alternate methods, Mathematical Journal of Interdisciplinary Sciences 6(1) (2017), 37 – 48, DOI: 10.15415/mjis.2017.61004.

F. T. Howard and F. Saidak, Zhou's theory of constructing identities, Congress Numer. 200 (2010), 225 – 237.

C. Kızılates, P. Catarino and N. Tuglu, On the bicomplex generalized Tribonacci quaternions, Mathematics 7(1) (2019), 80, DOI: 10.3390/math7010080.

M. E. Luna-Elizarrarás, M. Shapiro, D. C. Struppa and A. Vajiac, Bicomplex numbers and their elementary functions, CUBO A Mathematical Journal 14(2) (2012), 61 – 80, DOI: 10.4067/S0719-06462012000200004.

R. S. Melham, Some analogs of the identity (F^2_n+F^2_{n+1}+F^2_{2n+1}), Fibonacci Quarterly (1999), 305 – 311.

L. R. Natividad, On solving Fibonacci-like sequences of fourth, fifth and sixth order, International Journal of Mathematics and Computing 3(2) (2013), 38 – 40.

S. K. Nurkan and Ë™I. A. Güven, A note on bicomplex Fibonacci and Lucas numbers, International Journal of Pure and Applied Mathematics 120(3) (2018), 365 – 377, DOI: 10.12732/ijpam.v120i3.7.

S. K. Nurkan and Ë™I. A. Güven, A note on bicomplex Fibonacci and Lucas numbers, arXiv 1508.03972 [math.NT] (2015), https://arxiv.org/abs/1508.03972.

D. Rochon and M. Shapiro, On algebraic properties of Bicomplex and Hyperbolic numbers, Anal. Univ. Oradea Fascicola. Matematica. 11 (2004), 1 – 28.

B. Singh, P. Bhadouria, O. Sikhwal and K. Sisodiya, A formula for Tetranacci-like sequence, General Mathematics Notes 20(2) (2014), 136 – 141.

Y. Soykan, Gaussian generalized tetranacci numbers, arXiv 1902.03936 [math.NT] (2019), https://arxiv.org/abs/1902.03936.

M. E. Waddill, Another generalized Fibonacci sequence, Fibonacci Quarterly 5(3) (1967), 209 – 227.

M. E. Waddill, The tetranacci sequence and generalizations, Fibonacci Quarterly (1992), 9 – 20.

J. P. Ward, Quaternions and Cayley Numbers: Algebra and Applications, Kluwer Academic Publishers, London (1997), DOI: 0.1007/978-94-011-5768-1.

M. N. Zaveri and J. K. Patel, Binet's formula for the tetranacci sequence, International Journal of Science and Research (IJSR), 5(12) (2016), 1911 – 1914.

Downloads

Published

31-03-2020
CITATION

How to Cite

Soykan, Y. (2020). Bicomplex Tetranacci and Tetranacci-Lucas Quaternions. Communications in Mathematics and Applications, 11(1), 95–112. https://doi.org/10.26713/cma.v11i1.1212

Issue

Vol. 11 No. 1 (2020)

Section

Research Article

License

Creative Commons Licence 4.0 by  

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.