Araştırma Makalesi
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k- Gaussian Fibonacci sayılarının yeni bir ailesi

Yıl 2019, , 184 - 189, 15.03.2019
https://doi.org/10.25092/baunfbed.542440

Öz

Bu yazıda, yeni bir k - Gaussian Fibonacci sayıları ailesi tanımlanmış ve bu aile ile bilinen Gaussian Fibonacci sayıları arasında bazı ilişkiler bulunmuştur. Ayrıca, k=2 için bu ailenin üreteç fonksiyonlarını elde edilmiştir.

Kaynakça

  • Horadam, A.F., Complex Fibonacci Numbers and Fibonacci Quaternions, American Mathematics Monthly, 70, 289-291, (1963).
  • Berzsenyi, G., Gaussian Fibonacci numbers, The Fibonacci Quarterly,15, 223-236, (1977).
  • Mikkawy, M. and Sogabe, T., A new family of k-Fibonacci numbers, Applied Mathematics and Computation, 215, 4456-4461, (2010).
  • Karduman, E., On determinants of matrices with general Fibonacci numbers entries, Applied Mathematics and Computation, 167, 670–676, (2005).
  • Akbulak, M., Bozkurt, D., On the order-m generalized Fibonacci k-numbers, Chaos Soliton Fractal, 42(3), 1347-1355, (2009),.
  • Dunlap, R.A., The golden ratio and Fibonacci numbers, World Scientific Press, Singapore, 1997.
  • Falcon, S., Plaza, A., The k-Fibonacci sequence and the Pascal 2-triangle, Chaos Soliton Fractal, 33, 38–49, (2007).
  • Grabowski, A., Wojtecki, P., Lucas numbers and generalized Fibonacci numbers, Formalized Mathematics. 12, 329–334, (2004).
  • Kiliç, E., Tasci, D. Generalized order-k Fibonacci and Lucas numbers, Rocky Mountain Journal of Mathematics, 38, 1991–2008, (2008).
  • Öcal, A.A., Tuglu, N., Altinisik, E., On the representation of k-generalized Fibonacci and Lucas numbers, Applied Mathematics and Computation. 170, (2005).
  • Shiu, W.C., Lam, P.C.B., More on the generalized Fibonacci numbers and associated bipartite graphs, International Journal of Mathematics, 3, 5–9, (2003).
  • Stanimirovic, P.S., Nikolov, J., Stanimirovic, I., A generalization of Fibonacci and Lucas matrices, Discrete Applied Mathematics, 156 (2008) 2606–2619.
  • Falcon, S., Plaza, A., On k-Fibonacci numbers of arithmetic indexes, Applied Mathematics and Computation, 208 (2009) 180–185.
  • Deveci, Ö., Karaduman, E. and Campell, CM., On the k-nacci sequences in finite binary polyhedral groups, Algebra Colloquium, Vol. 18, pp. 945, 2011.
  • Falcon, S., Fibonacci’s multiplicative sequence, International Journal of Mathematical Education in Science and Technology. 34 (2) (2003) 310–315.
  • Sloane, N.J.A., The on-line encyclopedia of integer sequences, 2008.

A new family of k- Gaussian Fibonacci numbers

Yıl 2019, , 184 - 189, 15.03.2019
https://doi.org/10.25092/baunfbed.542440

Öz

In this manuscript, a new family of k- Gaussian Fibonacci numbers has been identified and some relationships between this family and known Gaussian Fibonacci numbers have been found. Also, I the generating functions of this family for k=2 has been obtained.

Kaynakça

  • Horadam, A.F., Complex Fibonacci Numbers and Fibonacci Quaternions, American Mathematics Monthly, 70, 289-291, (1963).
  • Berzsenyi, G., Gaussian Fibonacci numbers, The Fibonacci Quarterly,15, 223-236, (1977).
  • Mikkawy, M. and Sogabe, T., A new family of k-Fibonacci numbers, Applied Mathematics and Computation, 215, 4456-4461, (2010).
  • Karduman, E., On determinants of matrices with general Fibonacci numbers entries, Applied Mathematics and Computation, 167, 670–676, (2005).
  • Akbulak, M., Bozkurt, D., On the order-m generalized Fibonacci k-numbers, Chaos Soliton Fractal, 42(3), 1347-1355, (2009),.
  • Dunlap, R.A., The golden ratio and Fibonacci numbers, World Scientific Press, Singapore, 1997.
  • Falcon, S., Plaza, A., The k-Fibonacci sequence and the Pascal 2-triangle, Chaos Soliton Fractal, 33, 38–49, (2007).
  • Grabowski, A., Wojtecki, P., Lucas numbers and generalized Fibonacci numbers, Formalized Mathematics. 12, 329–334, (2004).
  • Kiliç, E., Tasci, D. Generalized order-k Fibonacci and Lucas numbers, Rocky Mountain Journal of Mathematics, 38, 1991–2008, (2008).
  • Öcal, A.A., Tuglu, N., Altinisik, E., On the representation of k-generalized Fibonacci and Lucas numbers, Applied Mathematics and Computation. 170, (2005).
  • Shiu, W.C., Lam, P.C.B., More on the generalized Fibonacci numbers and associated bipartite graphs, International Journal of Mathematics, 3, 5–9, (2003).
  • Stanimirovic, P.S., Nikolov, J., Stanimirovic, I., A generalization of Fibonacci and Lucas matrices, Discrete Applied Mathematics, 156 (2008) 2606–2619.
  • Falcon, S., Plaza, A., On k-Fibonacci numbers of arithmetic indexes, Applied Mathematics and Computation, 208 (2009) 180–185.
  • Deveci, Ö., Karaduman, E. and Campell, CM., On the k-nacci sequences in finite binary polyhedral groups, Algebra Colloquium, Vol. 18, pp. 945, 2011.
  • Falcon, S., Fibonacci’s multiplicative sequence, International Journal of Mathematical Education in Science and Technology. 34 (2) (2003) 310–315.
  • Sloane, N.J.A., The on-line encyclopedia of integer sequences, 2008.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Sait Taş Bu kişi benim 0000-0002-9815-8732

Yayımlanma Tarihi 15 Mart 2019
Gönderilme Tarihi 17 Eylül 2018
Yayımlandığı Sayı Yıl 2019

Kaynak Göster

APA Taş, S. (2019). A new family of k- Gaussian Fibonacci numbers. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 21(1), 184-189. https://doi.org/10.25092/baunfbed.542440
AMA Taş S. A new family of k- Gaussian Fibonacci numbers. BAUN Fen. Bil. Enst. Dergisi. Mart 2019;21(1):184-189. doi:10.25092/baunfbed.542440
Chicago Taş, Sait. “A New Family of K- Gaussian Fibonacci Numbers”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 21, sy. 1 (Mart 2019): 184-89. https://doi.org/10.25092/baunfbed.542440.
EndNote Taş S (01 Mart 2019) A new family of k- Gaussian Fibonacci numbers. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 21 1 184–189.
IEEE S. Taş, “A new family of k- Gaussian Fibonacci numbers”, BAUN Fen. Bil. Enst. Dergisi, c. 21, sy. 1, ss. 184–189, 2019, doi: 10.25092/baunfbed.542440.
ISNAD Taş, Sait. “A New Family of K- Gaussian Fibonacci Numbers”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 21/1 (Mart 2019), 184-189. https://doi.org/10.25092/baunfbed.542440.
JAMA Taş S. A new family of k- Gaussian Fibonacci numbers. BAUN Fen. Bil. Enst. Dergisi. 2019;21:184–189.
MLA Taş, Sait. “A New Family of K- Gaussian Fibonacci Numbers”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, c. 21, sy. 1, 2019, ss. 184-9, doi:10.25092/baunfbed.542440.
Vancouver Taş S. A new family of k- Gaussian Fibonacci numbers. BAUN Fen. Bil. Enst. Dergisi. 2019;21(1):184-9.

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