ON THE PROPERTIES OF NEW FAMILIES OF GENERALIZED FIBONACCI NUMBERS

In this paper, new families of generalized Fibonacci and Lucas numbers are introduced. In addition, we present the recurrence relations and the generating functions of the new families for $k=2$.

Keywords:

Horadam sequences, generalized Fibonacci numbers, generating ma- trix, generating function recurrence relations,

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[1] A. Atalay, K. Uslu and H. Gokkaya, New families of s- bonacci and s-lucas numbers, Selcuk Journal of Applied Mathematics, 14(2) (2013), 34-42.
[2] P. Catarino et al., New families of Jacobsthal and Jacobsthal-Lucas numbers, Algebra and Discrete Mathematics, 20(1) (2015), 40-54.
[3] G. Cerda-Morales, Matrix methods in Horadam sequences, Bol. Mat. 19 (2) (2012), 97-106.
[4] G. Cerda-Morales, On generalized Fibonacci and Lucas numbers by matrix methods, Hacettepe Journal of Mathematics and Statistics, 42(2) (2013), 173-179.
[5] M. El-Mikkawy and T. Sogabe, A new family of k-Fibonacci numbers, Applied Mathematics and Computation 215 (2010), 4456-4461.
[6] A.F. Horadam, Basic properties of a certain generalized sequence of numbers, Fibonacci Quart. 3 (1965), 161-176.
[7] A.F. Horadam, Jacobsthal representation numbers, Fibonacci Quart. Vol. 34(1) (1996), 40-53.
[8] D. Kalman and R. Mena, The Fibonacci numbers-exposed, Math. Mag., 76 (2003), 81-167.
[9] F. Koken and D. Bozkurt, On the Jacobsthal numbers by matrix methods, Int. J. Contemp. Math. Sci. 3(13) (2008), 605-614.
[10] E. Karaduman, On determinants of matrices with general Fibonacci numbers entries, Appl. Math. Comp. 167 (2005), 670-676.
[11] N. Yilmaz, Y. Yazlik and N. Taskara, On the k-Generalized Fibonacci Numbers, Selcuk Journal of Applied Mathematics, 13(1) (2012), 83-88.

Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2013
Yayıncı: Mehmet Zeki SARIKAYA

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