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Öğe Combinatorial Sums of Generalized Fibonacci and Lucas Numbers(CHARLES BABBAGE RES CTR, 2011) Uslu, K.; Taskara, N.; Gulec, H. H.In this study, we consider generalization of the well-known Fibonacci and Lucas numbers related with combinatorial sums by using finite differences. To write generalized Fibonacci and Lucas sequences in a new direct way, we investigate some new properties of these numbers.Öğe The Construction of Horadam Numbers in Terms of the Determinant of Tridiagonal Matrices(AMER INST PHYSICS, 2011) Taskara, N.; Uslu, K.; Yazlik, Y.; Yilmaz, N.In this study, by using determinants of tridiagonal matrices, we mainly obtain Horadam numbers with positive and negative indices. Therefore we establish a new generalization for the tridiagonal matrices that represent well known numbers such as Fibonacci, Lucas, Jacobsthal, Jacobsthal-Lucas, Pell and Pell-Lucas numbers.Öğe The Generalized (s, t)-Sequence and its Matrix Sequence(AMER INST PHYSICS, 2011) Yazlik, Y.; Taskara, N.; Uslu, K.; Yilmaz, N.In this study, we first define a new sequence in which it generalizes (s, t)-Fibonacci and (s, t)-Lucas sequences at the same time. After that, by using it, we establish generalized (s, t)-matrix sequences. Finally we present some important relationships among this new generalization, (s, t)-Fibonacci and (s, t)-Lucas sequences and their matrix sequences.Öğe The Generalized k-Fibonacci and k-Lucas Numbers(CHARLES BABBAGE RES CTR, 2011) Uslu, K.; Taskara, N.; Kose, H.In this paper we give the generalization {G(k,n)}(n is an element of N) of k-Fibonacci and k-Lucas numbers. After that, by using this generalization, it has been obtained some new algebraic properties on these numbers.Öğe JACOBSTHAL FAMILY MODULO m(2016) Yılmaz, N.; Taskara, N.; Yazlık, Y.; Uslu, K.In this study, we investigate sets of remainder of the Jacobsthal and JacobsthalLucas numbers modulo m for some positive integers m. Also some properties related tothese sets and a new method to calculate the length of period modulo m is given.Öğe A new approach to generalized Fibonacci and Lucas numbers with binomial coefficients(ELSEVIER SCIENCE INC, 2013) Gulec, H. H.; Taskara, N.; Uslu, K.In this study, Fibonacci and Lucas numbers have been obtained by using generalized Fibonacci numbers. In addition, some new properties of generalized Fibonacci numbers with binomial coefficients have been investigated to write generalized Fibonacci sequences in a new direct way. Furthermore, it has been given a new formula for some Lucas numbers. (C) 2013 Elsevier Inc. All rights reserved.Öğe On the Binomial Sums of k-Fibonacci and k-Lucas sequences(AMER INST PHYSICS, 2011) Yilmaz, N.; Taskara, N.; Uslu, K.; Yazlik, Y.The main purpose of this paper is to establish some new properties of k-Fibonacci and k-Lucas numbers in terms of binomial sums. By that, we can obtain these special numbers in a new and direct way. Moreover, some connections between k-Fibonacci and k-Lucas numbers are revealed to get a more strong result.Öğe On the norms of circulant matrices with the Fibonacci and Lucas numbers (vol 160, pg 125, 2005) -2(ELSEVIER SCIENCE INC, 2007) Uslu, K.; Nalli, A.; Sen, M.[Abstract not Available]Öğe On the Properties of Lucas Numbers With Binomial Coefficients(Pergamon-Elsevier Science Ltd, 2010) Taşkara, Necati; Uslu, K.; Güleç, H. H.In this study, some new properties of Lucas numbers with binomial coefficients have been obtained to write Lucas sequences in a new direct way. In addition, some important consequences of these results related to the Fibonacci numbers have been given.Öğe The periodicity and solutions of the rational difference equation with periodic coefficients(PERGAMON-ELSEVIER SCIENCE LTD, 2011) Taskara, N.; Uslu, K.; Tollu, D. T.In this paper, we give necessary and sufficient conditions for generalized solution and periodicity of the difference equation x(n+1) = p(n)x(n-k)+x(n-(k+1))/q(n)+x(n-(k+1)) with (k + 2)-periodic coefficients, where k is an element of N, x(-k-1), x(-k,) ... ,x(0) is an element of R. Also, we obtain that the generalized solution is periodic with (k + 1)-period. (C) 2011 Elsevier Ltd. All rights reserved.Öğe The relations among k-Fibonacci, k-Lucas and generalized k-Fibonacci numbers and the spectral norms of the matrices of involving these numbers(CHARLES BABBAGE RES CTR, 2011) Uslu, K.; Taskara, N.; Uygun, S.In this study, we obtain the relations among k-Fibonacci, k-Lucas and generalized k-Fibonacci numbers. Then we define circulant matrices involving k-Lucas and generelized k-Fibonacci numbers. In the last of this study, we investigate the upper and lower bounds for the norms these matrices.Öğe The (s, t) Jacobsthal and (s, t) Jacobsthal-Lucas Matrix Sequences(CHARLES BABBAGE RES CTR, 2013) Uslu, K.; Uygun, S.In this study, we first define new sequences named (s, t)-Jacobsthal and (s, t) Jacobsthal-Lucas sequences. After that, by using these sequences, we establish (s,t)-Jacobsthal and (s, t) Jacobsthal-Lucas matrix sequences. Finally we present some important relationships between these matrix sequences.Öğe The Solutions of the Periodic Rational Recursive Systems(RGN PUBL, 2016) Uslu, K.; Kilic, E.In this study, we obtain the solutions of some periodic rational difference equation systems. Then we examinate the period of solutions of these systems.
