Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2015, Cilt: 3 Sayı: 2, 20 - 26, 30.10.2015
https://doi.org/10.36753/mathenot.421323

Öz

Kaynakça

  • [1] Bolat, C. and Köse H., On the properties of k−Fibonacci numbers, Int. J. Contemp. Math. Sciences, 5, 1097-1105, (2010).
  • [2] Falcon S., On the k−Lucas Numbers, Int. J. Contemp. Math. Sciences, 6, 1039-1050, (2011).
  • [3] Hoggatt V. E., Generalized Zeckendorf theorem, Fibonacci Quart 10, 89-93, (1972).
  • [4] James P., When is a number Fibonacci?, Department of Computer Science, Swansea University, January 25, (2009).
  • [5] Kalman, D. and Mena, R., The Fibonacci numbers-exposed. Math. Mag. 76, no. 3, 167-181, (2003).
  • [6] Cahill N. D., D’Errico J. R., Spence J. S., Complex factorizations of the Fibonacci and Lucas numbers, Fibonacci Quart. 41, no. 1, 13-19, (2003).
  • [7] Ismail, M. E. H., One parameter generalizations of the Fibonacci and Lucas numbers, Fibonacci Quart. 46/47, no. 2, 167-180, (2008/09).
  • [8] Koshy T., Fibonacci and Lucas numbers with applications, Wiley, (2001).
  • [9] Siar Z., Keskin R., Some new identites concerning Generalized Fibonacci and Lucas Numbers, Hacet. J. Math. Stat. 42, no.3, 211-222, (2013).
  • [10] Ozgur, N. Y., Ucar S., Oztunc O., Complex Factorizations of the k−Fibonacci and k−Lucas numbers, in press, (2015).
  • [11] S. Falcon and A. Plaza, On the Fibonacci k-numbers, ` Chaos, Solitons & Fractals 32, 1615- 1624 (2007).
  • [12] S. Falcon and A. Plaza, The k-Fibonacci sequence and the Pascal 2-triangle, ` Chaos, Solitons & Fractals 33, 38-49 (2007).
  • [13] MATLAB trial version 8.5.0. Natick, Massachusetts: The MathWorks Inc., (2015

ON DETERMINATION OF k-FIBONACCI AND k-LUCAS NUMBERS

Yıl 2015, Cilt: 3 Sayı: 2, 20 - 26, 30.10.2015
https://doi.org/10.36753/mathenot.421323

Öz

In this study we investigate some properties of the k-Fibonacci
and k-Lucas sequences which are generalize the classical Fibonacci and Lucas
sequences. Moreover, two efficient tests are introduced as to whether or not a
positive integer is k-Fibonacci or k-Lucas. 

Kaynakça

  • [1] Bolat, C. and Köse H., On the properties of k−Fibonacci numbers, Int. J. Contemp. Math. Sciences, 5, 1097-1105, (2010).
  • [2] Falcon S., On the k−Lucas Numbers, Int. J. Contemp. Math. Sciences, 6, 1039-1050, (2011).
  • [3] Hoggatt V. E., Generalized Zeckendorf theorem, Fibonacci Quart 10, 89-93, (1972).
  • [4] James P., When is a number Fibonacci?, Department of Computer Science, Swansea University, January 25, (2009).
  • [5] Kalman, D. and Mena, R., The Fibonacci numbers-exposed. Math. Mag. 76, no. 3, 167-181, (2003).
  • [6] Cahill N. D., D’Errico J. R., Spence J. S., Complex factorizations of the Fibonacci and Lucas numbers, Fibonacci Quart. 41, no. 1, 13-19, (2003).
  • [7] Ismail, M. E. H., One parameter generalizations of the Fibonacci and Lucas numbers, Fibonacci Quart. 46/47, no. 2, 167-180, (2008/09).
  • [8] Koshy T., Fibonacci and Lucas numbers with applications, Wiley, (2001).
  • [9] Siar Z., Keskin R., Some new identites concerning Generalized Fibonacci and Lucas Numbers, Hacet. J. Math. Stat. 42, no.3, 211-222, (2013).
  • [10] Ozgur, N. Y., Ucar S., Oztunc O., Complex Factorizations of the k−Fibonacci and k−Lucas numbers, in press, (2015).
  • [11] S. Falcon and A. Plaza, On the Fibonacci k-numbers, ` Chaos, Solitons & Fractals 32, 1615- 1624 (2007).
  • [12] S. Falcon and A. Plaza, The k-Fibonacci sequence and the Pascal 2-triangle, ` Chaos, Solitons & Fractals 33, 38-49 (2007).
  • [13] MATLAB trial version 8.5.0. Natick, Massachusetts: The MathWorks Inc., (2015
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Nihal Yilmaz Özgür Bu kişi benim

Öznur Öztunç Kaymak Bu kişi benim

Yayımlanma Tarihi 30 Ekim 2015
Gönderilme Tarihi 8 Temmuz 2015
Yayımlandığı Sayı Yıl 2015 Cilt: 3 Sayı: 2

Kaynak Göster

APA Özgür, N. Y., & Kaymak, Ö. Ö. (2015). ON DETERMINATION OF k-FIBONACCI AND k-LUCAS NUMBERS. Mathematical Sciences and Applications E-Notes, 3(2), 20-26. https://doi.org/10.36753/mathenot.421323
AMA Özgür NY, Kaymak ÖÖ. ON DETERMINATION OF k-FIBONACCI AND k-LUCAS NUMBERS. Math. Sci. Appl. E-Notes. Ekim 2015;3(2):20-26. doi:10.36753/mathenot.421323
Chicago Özgür, Nihal Yilmaz, ve Öznur Öztunç Kaymak. “ON DETERMINATION OF K-FIBONACCI AND K-LUCAS NUMBERS”. Mathematical Sciences and Applications E-Notes 3, sy. 2 (Ekim 2015): 20-26. https://doi.org/10.36753/mathenot.421323.
EndNote Özgür NY, Kaymak ÖÖ (01 Ekim 2015) ON DETERMINATION OF k-FIBONACCI AND k-LUCAS NUMBERS. Mathematical Sciences and Applications E-Notes 3 2 20–26.
IEEE N. Y. Özgür ve Ö. Ö. Kaymak, “ON DETERMINATION OF k-FIBONACCI AND k-LUCAS NUMBERS”, Math. Sci. Appl. E-Notes, c. 3, sy. 2, ss. 20–26, 2015, doi: 10.36753/mathenot.421323.
ISNAD Özgür, Nihal Yilmaz - Kaymak, Öznur Öztunç. “ON DETERMINATION OF K-FIBONACCI AND K-LUCAS NUMBERS”. Mathematical Sciences and Applications E-Notes 3/2 (Ekim 2015), 20-26. https://doi.org/10.36753/mathenot.421323.
JAMA Özgür NY, Kaymak ÖÖ. ON DETERMINATION OF k-FIBONACCI AND k-LUCAS NUMBERS. Math. Sci. Appl. E-Notes. 2015;3:20–26.
MLA Özgür, Nihal Yilmaz ve Öznur Öztunç Kaymak. “ON DETERMINATION OF K-FIBONACCI AND K-LUCAS NUMBERS”. Mathematical Sciences and Applications E-Notes, c. 3, sy. 2, 2015, ss. 20-26, doi:10.36753/mathenot.421323.
Vancouver Özgür NY, Kaymak ÖÖ. ON DETERMINATION OF k-FIBONACCI AND k-LUCAS NUMBERS. Math. Sci. Appl. E-Notes. 2015;3(2):20-6.

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