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.
Anahtar Kelimeler
Fibonacci sayıları Gaussian Fibonacci sayıları Gaussian sayıları
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.
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.
Anahtar Kelimeler
Fibonacci numbers Gaussian fibonacci numbers Gaussian numbers
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.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Yayımlanma Tarihi | 15 Mart 2019 |
| Gönderilme Tarihi | 17 Eylül 2018 |
| Yayımlandığı Sayı | Yıl 2019 Cilt: 21 Sayı: 1 |