k- Gaussian Fibonacci sayılarının yeni bir ailesi

Abstract

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.

Keywords

• Fibonacci sayıları,Gaussian Fibonacci sayıları,Gaussian sayıları

A new family of k- Gaussian Fibonacci numbers

Abstract

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.

Keywords

• Fibonacci numbers,Gaussian fibonacci numbers,Gaussian numbers

References

1. Horadam, A.F., Complex Fibonacci Numbers and Fibonacci Quaternions, American Mathematics Monthly, 70, 289-291, (1963).
2. Berzsenyi, G., Gaussian Fibonacci numbers, The Fibonacci Quarterly,15, 223-236, (1977).
3. Mikkawy, M. and Sogabe, T., A new family of k-Fibonacci numbers, Applied Mathematics and Computation, 215, 4456-4461, (2010).
4. Karduman, E., On determinants of matrices with general Fibonacci numbers entries, Applied Mathematics and Computation, 167, 670–676, (2005).
5. Akbulak, M., Bozkurt, D., On the order-m generalized Fibonacci k-numbers, Chaos Soliton Fractal, 42(3), 1347-1355, (2009),.
6. Dunlap, R.A., The golden ratio and Fibonacci numbers, World Scientific Press, Singapore, 1997.
7. Falcon, S., Plaza, A., The k-Fibonacci sequence and the Pascal 2-triangle, Chaos Soliton Fractal, 33, 38–49, (2007).
8. Grabowski, A., Wojtecki, P., Lucas numbers and generalized Fibonacci numbers, Formalized Mathematics. 12, 329–334, (2004).

9. Kiliç, E., Tasci, D. Generalized order-k Fibonacci and Lucas numbers, Rocky Mountain Journal of Mathematics, 38, 1991–2008, (2008).
10. Öcal, A.A., Tuglu, N., Altinisik, E., On the representation of k-generalized Fibonacci and Lucas numbers, Applied Mathematics and Computation. 170, (2005).
11. 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).
12. Stanimirovic, P.S., Nikolov, J., Stanimirovic, I., A generalization of Fibonacci and Lucas matrices, Discrete Applied Mathematics, 156 (2008) 2606–2619.
13. Falcon, S., Plaza, A., On k-Fibonacci numbers of arithmetic indexes, Applied Mathematics and Computation, 208 (2009) 180–185.
14. Deveci, Ö., Karaduman, E. and Campell, CM., On the k-nacci sequences in finite binary polyhedral groups, Algebra Colloquium, Vol. 18, pp. 945, 2011.
15. Falcon, S., Fibonacci’s multiplicative sequence, International Journal of Mathematical Education in Science and Technology. 34 (2) (2003) 310–315.
16. Sloane, N.J.A., The on-line encyclopedia of integer sequences, 2008.