Bicomplex Tetranacci and Tetranacci-Lucas Quaternions
DOI:
https://doi.org/10.26713/cma.v11i1.1212Keywords:
Bicomplex Tetranacci numbers, Bicomplex quaternions, Bicomplex Tetranacci quaternions, Bicomplex Tetranacci-Lucas quaternionsAbstract
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
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
Issue
Section
License
How to Cite
