Gauss Narayana-Lucas Sayıları Üzerine

Nusret Karaaslan; Merve Nur Fazlıoğlu

doi:10.29002/asujse.1020770

Research Article

On the Gaussian Narayana-Lucas Numbers

Year 2021, Volume: 5 Issue: 2, 125 - 137, 30.12.2021

Nusret Karaaslan , Merve Nur Fazlıoğlu

https://doi.org/10.29002/asujse.1020770

Abstract

In this study, the Gauss Narayana-Lucas number sequence is introduced and examined. Firstly, the Gaussian Narayana-Lucas number sequence is defined by extending the Narayana-Lucas number sequence. Then, the generating function and the Binet formula of this number sequence were obtained. In addition, some sum formulas related to the Gaussian Narayana-Lucas number sequence and some matrices containing the terms of this sequence are examined. Finally, some relations were obtained between Gaussian Narayana and Gaussian Narayana-Lucas number sequences.

Keywords

Narayana numbers, Narayana-Lucas numbers, Gaussian Narayana-Lucas numbers, generating function, Binet formula

References

[1] T. Koshy, Fibonacci and Lucas Numbers with Applications (John Wiley and Sons Inc., New York, 2001) pp. 51-131.
[2] V. E. Hoggatt Jr., Fibonacci and Lucas Numbers (Houghton Mifflin, Boston, 1969).
[3] T. Koshy, Pell and Pell-Lucas Numbers with Applications (Springer, New York, 2014).
[4] T. Yağmur, New Approach to Pell and Pell-Lucas Sequences. Kyungpook Mathematical Journal 59(1) (2019) 23-34.
[5] A. F. Horadam, Jacobsthal Representation Numbers. Fibonacci Quarterly 34 (1996) 40-54.
[6] A. F. Horadam, Complex Fibonacci Numbers and Fibonacci Quaternions. American Mathematics Monthly 70 (1963) 289-291.
[7] I. J. Good, Complex Fibonacci and Lucas Numbers, Continued Fractions, and the Square Root of the Golden Ratio. Fibonacci Quarterly 31(1) (1993) 7-20.
[8] J. H. Jordan, Gaussian Fibonacci and Lucas Numbers. Fibonacci Quarterly 3 (1965) 315-318.
[9] S. Halıcı, S. Öz, On Gaussian Pell and Pell-Lucas Numbers. Ordu University Science and Technology Journal 6(1) (2016) 8-18.
[10] T. Yağmur, N. Karaaslan, Gaussian Modified Pell Sequence and Gaussian Modified Pell Polynomial Sequence. Aksaray University Journal of Science and Engineering 2(1) (2018) 63-72.
[11] M. Aşçı, E. Gürel, Gaussian Jacobsthal and Gaussian Jacobsthal-Lucas Numbers. Ars Combinatoria 111 (2013) 53-63.
[12] A. G. Shannon, P. G. Anderson, A F. Horadam, Properties of Cordonnier, Perrin and Van der Laan Numbers. International Journal of Mathematical Education in Science and Technology 37(7) (2006) 825-831.
[13] D. Taşçı, Padovan and Pell-Padovan Quaternions. Journal of Science and Arts 1(42) (2018) 125-132.
[14] Y. Soykan, On Generalized Narayana Numbers. Int. J. Adv. Appl. Math. And Mech. 7(3) (2020) 43-56.
[15] N. J. A. Sloane, On-line Encyclopedia of Integer Sequences. http://oeis.org/
[16] D. Taşçı, Gaussian Padovan and and Gaussian Pell-Padovan Sequences. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67(2) (2018) 82-88.
[17] M. Y. Kartal, Gaussian Padovan and Gaussian Perrin Numbers and Properties of Them. Asian-European Journal of Mathematics 12(6) (2019) 2040014.
[18] E. Özkan, B. Kuloğlu, On The New Narayana Polynomials, The Gauss Narayana Numbers and Their Polynomials. Asian-European Journal of Mathematics 14(6) (2021) 2150100.