TY - JOUR T1 - A new family of k- Gaussian Fibonacci numbers TT - k- Gaussian Fibonacci sayılarının yeni bir ailesi AU - Taş, Sait PY - 2019 DA - March DO - 10.25092/baunfbed.542440 JF - Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi JO - BAUN Fen. Bil. Enst. Dergisi PB - Balıkesir University WT - DergiPark SN - 1301-7985 SP - 184 EP - 189 VL - 21 IS - 1 LA - en AB - 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. KW - Fibonacci numbers KW - Gaussian fibonacci numbers KW - Gaussian numbers N2 - 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. CR - Horadam, A.F., Complex Fibonacci Numbers and Fibonacci Quaternions, American Mathematics Monthly, 70, 289-291, (1963). CR - Berzsenyi, G., Gaussian Fibonacci numbers, The Fibonacci Quarterly,15, 223-236, (1977). CR - Mikkawy, M. and Sogabe, T., A new family of k-Fibonacci numbers, Applied Mathematics and Computation, 215, 4456-4461, (2010). CR - Karduman, E., On determinants of matrices with general Fibonacci numbers entries, Applied Mathematics and Computation, 167, 670–676, (2005). CR - Akbulak, M., Bozkurt, D., On the order-m generalized Fibonacci k-numbers, Chaos Soliton Fractal, 42(3), 1347-1355, (2009),. CR - Dunlap, R.A., The golden ratio and Fibonacci numbers, World Scientific Press, Singapore, 1997. CR - Falcon, S., Plaza, A., The k-Fibonacci sequence and the Pascal 2-triangle, Chaos Soliton Fractal, 33, 38–49, (2007). CR - Grabowski, A., Wojtecki, P., Lucas numbers and generalized Fibonacci numbers, Formalized Mathematics. 12, 329–334, (2004). CR - Kiliç, E., Tasci, D. Generalized order-k Fibonacci and Lucas numbers, Rocky Mountain Journal of Mathematics, 38, 1991–2008, (2008). CR - Öcal, A.A., Tuglu, N., Altinisik, E., On the representation of k-generalized Fibonacci and Lucas numbers, Applied Mathematics and Computation. 170, (2005). CR - 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). CR - Stanimirovic, P.S., Nikolov, J., Stanimirovic, I., A generalization of Fibonacci and Lucas matrices, Discrete Applied Mathematics, 156 (2008) 2606–2619. CR - Falcon, S., Plaza, A., On k-Fibonacci numbers of arithmetic indexes, Applied Mathematics and Computation, 208 (2009) 180–185. CR - Deveci, Ö., Karaduman, E. and Campell, CM., On the k-nacci sequences in finite binary polyhedral groups, Algebra Colloquium, Vol. 18, pp. 945, 2011. CR - Falcon, S., Fibonacci’s multiplicative sequence, International Journal of Mathematical Education in Science and Technology. 34 (2) (2003) 310–315. CR - Sloane, N.J.A., The on-line encyclopedia of integer sequences, 2008. UR - https://doi.org/10.25092/baunfbed.542440 L1 - https://dergipark.org.tr/en/download/article-file/675293 ER -