Research Article
PDF Zotero Mendeley EndNote BibTex Cite

Gauss Narayana-Lucas Sayıları Üzerine

Year 2021, Volume 5, Issue 2, 125 - 137, 30.12.2021
https://doi.org/10.29002/asujse.1020770

Abstract

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.

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.

On the Gaussian Narayana-Lucas Numbers

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

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.

Details

Primary Language Turkish
Subjects Basic Sciences
Journal Section Research Article
Authors

Nusret KARAASLAN (Primary Author)
KALKANDERE DAĞDİBİ ORTAOKULU
0000-0002-0244-1286
Türkiye


Merve Nur FAZLIOĞLU This is me
KALKANDERE ANADOLU İMAM HATİP LİSESİ
Türkiye

Publication Date December 30, 2021
Application Date November 8, 2021
Acceptance Date December 9, 2021
Published in Issue Year 2021, Volume 5, Issue 2

Cite

Bibtex @research article { asujse1020770, journal = {Aksaray University Journal of Science and Engineering}, issn = {}, eissn = {2587-1277}, address = {Aksaray Üniversitesi, Fen Bilimleri Enstitüsü, Merkez Kampüs, 68100 Aksaray}, publisher = {Aksaray University}, year = {2021}, volume = {5}, pages = {125 - 137}, doi = {10.29002/asujse.1020770}, title = {Gauss Narayana-Lucas Sayıları Üzerine}, key = {cite}, author = {Karaaslan, Nusret and Fazlıoğlu, Merve Nur} }
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
MLA Karaaslan, N. , Fazlıoğlu, M. N. "Gauss Narayana-Lucas Sayıları Üzerine" . Aksaray University Journal of Science and Engineering 5 (2021 ): 125-137 <http://asujse.aksaray.edu.tr/en/pub/issue/63258/1020770>
Chicago Karaaslan, N. , Fazlıoğlu, M. N. "Gauss Narayana-Lucas Sayıları Üzerine". Aksaray University Journal of Science and Engineering 5 (2021 ): 125-137
RIS TY - JOUR T1 - Gauss Narayana-Lucas Sayıları Üzerine AU - Nusret Karaaslan , Merve Nur Fazlıoğlu Y1 - 2021 PY - 2021 N1 - doi: 10.29002/asujse.1020770 DO - 10.29002/asujse.1020770 T2 - Aksaray University Journal of Science and Engineering JF - Journal JO - JOR SP - 125 EP - 137 VL - 5 IS - 2 SN - -2587-1277 M3 - doi: 10.29002/asujse.1020770 UR - https://doi.org/10.29002/asujse.1020770 Y2 - 2021 ER -
EndNote %0 Aksaray University Journal of Science and Engineering Gauss Narayana-Lucas Sayıları Üzerine %A Nusret Karaaslan , Merve Nur Fazlıoğlu %T Gauss Narayana-Lucas Sayıları Üzerine %D 2021 %J Aksaray University Journal of Science and Engineering %P -2587-1277 %V 5 %N 2 %R doi: 10.29002/asujse.1020770 %U 10.29002/asujse.1020770
ISNAD Karaaslan, Nusret , Fazlıoğlu, Merve Nur . "Gauss Narayana-Lucas Sayıları Üzerine". Aksaray University Journal of Science and Engineering 5 / 2 (December 2021): 125-137 . https://doi.org/10.29002/asujse.1020770
AMA Karaaslan N. , Fazlıoğlu M. N. Gauss Narayana-Lucas Sayıları Üzerine. Aksaray J. Sci. Eng.. 2021; 5(2): 125-137.
Vancouver Karaaslan N. , Fazlıoğlu M. N. Gauss Narayana-Lucas Sayıları Üzerine. Aksaray University Journal of Science and Engineering. 2021; 5(2): 125-137.
IEEE N. Karaaslan and M. N. Fazlıoğlu , "Gauss Narayana-Lucas Sayıları Üzerine", Aksaray University Journal of Science and Engineering, vol. 5, no. 2, pp. 125-137, Dec. 2021, doi:10.29002/asujse.1020770

Aksaray J. Sci. Eng. | e-ISSN: 2587-1277 | Period: Biannually | Founded: 2017 | Publisher: Aksaray University | https://asujse.aksaray.edu.tr




ASUJSE is indexing&Archiving in

crossref-logo-landscape-100.pngscilitLogo.png    scholar_logo_30dp.png   logo_wcmasthead_en.png   logo-large-explore.png    oaliblogo2.jpg   GettyImages_90309427_montage_255x130px.png search-result-logo-horizontal-TEST.jpgIndex Copernicus

22644



Creative Commons License