Aksaray University Journal of Science and Engineering
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Gauss Narayana-Lucas Sayıları Üzerine

Yıl 2021, Cilt: 5 Sayı: 2, 125 - 137, 30.12.2021

Nusret KARAASLAN Merve Nur FAZLIOĞLU

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

Öz

Bu çalışmada, Gauss Narayana-Lucas sayı dizisi tanıtıldı ve incelendi. İlk olarak Narayana-Lucas sayı dizisi genişletilerek Gauss Narayana-Lucas sayı dizisi tanımlanmıştır. Daha sonra bu sayı dizisine ait üreteç fonksiyonu ve Binet formülü elde edilmiştir. Ayrıca Gauss Narayana-Lucas sayı dizisi ile ilgili bazı toplam formülleri ve bu dizinin terimlerini içeren bazı matrisler araştırılmıştır. Son olarak Gauss Narayana ile Gauss Narayana-Lucas sayı dizileri arasında bazı ilişkiler elde edilmiştir.

Anahtar Kelimeler

Narayana sayı dizisi, Narayana-Lucas sayı dizisi, Gauss Narayana-Lucas sayı dizisi, üreteç fonksiyonu, Binet formülü

Kaynakça

  • [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.

On the Gaussian Narayana-Lucas Numbers

Yıl 2021, Cilt: 5 Sayı: 2, 125 - 137, 30.12.2021

Nusret KARAASLAN Merve Nur FAZLIOĞLU

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

Öz

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.

Anahtar Kelimeler

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

Kaynakça

  • [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.

Ayrıntılar

Birincil Dil Türkçe
Bölüm Research Article
Yazarlar

Nusret KARAASLAN
KALKANDERE DAĞDİBİ ORTAOKULU
0000-0002-0244-1286
Türkiye

Merve Nur FAZLIOĞLU
KALKANDERE ANADOLU İMAM HATİP LİSESİ
Türkiye

Yayımlanma Tarihi 30 Aralık 2021
Gönderilme Tarihi 8 Kasım 2021
Kabul Tarihi 9 Aralık 2021
Yayınlandığı Sayı Yıl 2021Cilt: 5 Sayı: 2

Kaynak Göster

APA Karaaslan, N. & Fazlıoğlu, M. N. (2021). Gauss Narayana-Lucas Sayıları Üzerine . Aksaray University Journal of Science and Engineering , 5 (2) , 125-137 . DOI: 10.29002/asujse.1020770
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