Generalized Tetranacci hybrid numbers

Yüksel Soykan; Erkan Taşdemir

Published: 2020-10-06

Vol. 35 No. 1 (2021)

Generalized Tetranacci hybrid numbers

Yüksel Soykan , Erkan Taşdemir

Abstract

In this paper, we introduce the generalized Tetranacci hybrid numbers and, as special cases, Tetranacci and Tetranacci-Lucas hybrid numbers. Moreover, we present Binet’s formulas, generating functions, and the summation formulas for those hybrid numbers.

Keywords:

Tetranacci numbers , hybrid numbers , Tetranacci hybrid numbers , Tetranacci-Lucas hybrid numbers

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Soykan, Y., & Taşdemir, E. (2020). Generalized Tetranacci hybrid numbers. Annales Mathematicae Silesianae, 35(1), 113–130. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13478

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References

1. J.B. Bacani and J.F.T. Rabago, On generalized Fibonacci numbers, Applied Mathematical Sciences 9 (2015), no. 73, 3611–3622.
2. R. Ben Taher and M. Rachidi, Explicit formulas for the constituent matrices. Application to the matrix functions, Spec. Matrices 3 (2015), 43–52.
3. R. Ben Taher and M. Rachidi, Solving some generalized Vandermonde systems and inverse of their associate matrices via new approaches for the Binet formula, Appl. Math. Comput. 290 (2016), 267–280.
4. B. Bernoussi, M. Rachidi, and O. Saeki, Factorial Binet formula and distributional moment formulation of generalized Fibonacci sequences, Fibonacci Quart. 42 (2004), no. 4, 320–329.
5. G. Cerda-Morales, Investigation of generalized hybrid Fibonacci numbers and their properties, arXiv preprint. Available at arXiv: 1806.02231v1.
6. G. Dattoli, S. Licciardi, R.M. Pidatella, and E. Sabia, Hybrid complex numbers: the matrix version, Adv. Appl. Clifford Algebr. 28 (2018), no. 3, Paper No. 58, 17 pp.
7. G.P.B. Dresden and Z. Du, A simplified Binet formula for k-generalized Fibonacci numbers, J. Integer Seq. 17 (2014), no. 4, Artlicle 14.4.7, 9 pp.
8. F. Dubeau, W. Motta, and M. Rachidi, O. Saeki, On weighted r-generalized Fibonacci sequences, Fibonacci Quart. 35 (1997), no. 2, 102–110.
9. 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 (2017), no. 1, 37–48.
10. F.T. Howard and F. Saidak, Zhou’s theory of constructing identities, Congr. Numer. 200 (2010), 225–237.
11. R.S. Melham, Some analogs of the identity F^2_n + F^2_{n+1} = F^2_{2n+1}, Fibonacci Quart. 37 (1999), no. 4, 305–311.
12. L.R. Natividad, On solving Fibonacci-like sequences of fourth, fifth and sixth order, Int. J. Math. Sci. Comput. 3 (2013), no. 2, 38–40.
13. M. Özdemir, Introduction to hybrid numbers, Adv. Appl. Clifford Algebr. 28 (2018), no. 1, Paper No. 11, 32 pp.
14. M. Özdemir, Finding n-th roots of a 2x2 real matrix using de Moivre’s formula, Adv. Appl. Clifford Algebr. 29 (2019), no. 1, Paper No. 2, 25 pp.
15. B. Singh, P. Bhadouria, O. Sikhwal, and K. Sisodiya, A formula for Tetranacci-like sequence, Gen. Math. Notes 20 (2014), no. 2, 136–141.
16. Y. Soykan, Gaussian generalized Tetranacci numbers, Journal of Advances in Mathematics and Computer Science 31 (2019), no. 3, Article no. JAMCS.48063, 21 pp.
17. A. Szynal-Liana, The Horadam hybrid numbers, Discuss. Math. Gen. Algebra Appl. 38 (2018), no. 1, 91–98.
18. A. Szynal-Liana and I. Włoch, On Jacobsthal and Jacobsthal-Lucas hybrid numbers, Ann. Math. Sil. 33 (2019), 276–283.
19. M.E. Waddill, The Tetranacci sequence and generalizations, Fibonacci Quart. 30 (1992), no. 1, 9–20.
20. M.E. Waddill and L. Sacks, Another generalized Fibonacci sequence, Fibonacci Quart. 5 (1967), no. 3, 209–222.
21. M.N. Zaveri and J.K. Patel, Binet’s formula for the Tetranacci sequence, International Journal of Science and Research (IJSR) 5 (2016), no. 12, 1911–1914. Google Scholar

Yüksel Soykan

Affiliation:

Department of Mathematics, Art and Science Faculty, Zonguldak Bülent Ecevit University, Turkey Turkey

Erkan Taşdemir

erkantasdemir@hotmail.com
https://orcid.org/0000-0002-5002-3193

Affiliation:

Pınarhisar Vocational School of Higher Education, Kırklareli University, Turkey Turkey

Vol. 35 No. 1 (2021)
Published: 2021-02-10

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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