Year 2016,
Volume: 9 Issue: 1, 95 - 101, 20.06.2016
Abstract
In this paper, it was showed that Fibonacci sequences {F_n^((k,p))} of a new family defined in [10] are a simply periodic sequences according to modulo p. We give some relationship between the family and ordinary Fibonacci numbers. Also, we prove some theorems concerning a new family and Lucas numbers.
References
- Arı, K., 2015. On h(x)-Lucas Quaternion Polynomials. Ars Combinatoria, 121, 291-303.
- Campbell, C. M., Campbell, P. P., 2005. The Fibonacci length of certain centro- polyhedral groups. Journal of Applied Mathematics and Computing 19, No.1-2, 231-240.
- Deveci, Ö., 2011. The Polytopic sequences in finite groups. Discrete Dynamics in Nature and Society Vol. 2011, 12 pages.
- Deveci, Ö., 2015. The Pell-padovan sequences and The Jacobsthal-Padovan seuences in finite groups. Util. Math. 98, 257-270.
- Grabowski, A., Wojtecki, P., 2004. Lucas numbers and generalized Fibonacci numbers. Form. Math. 12, 329–334.
- İpek, A., Arı, K., 2014. On Hessenberg and pentadiagonal determinants related with Fibonacci and Fibonacci-like numbers. Applied Mathematics and Computation, 229 (25), 433-439.
- İpek, A., Arı, K., 2015. On h(x)-Fibonacci octonion polynomials. Alabama Journal of Mathematics, 39.
- Kılıç, E., Tasci, D., 2006. On the Generalized Order-k Fibonacci and Lucas Numbers. Rocky Mountain Journal of Mathematics, 36, 1915-1926.
- Knox, S. W., 1992. Fibonacci Sequences In Finite groups. Fibonacci Quart., 30 No:2, 116-120.
- Lee, G. Y., 2000. k-Lucas numbers and associated bipartite graph. Linear Algebra and its Applications 320, 51–61.
- Lü, K., Wang, J., 2007. k-step Fibonacci sequence modulo m. Util. Math. 71, 169-178.
- Mikkawy, M., Sogabe, T., 2010. A new family of k-Fibonacci numbers. Applied Mathematics and Computation 215, 4456–4461.
- Stanimirovic, P. S., Nikolov J., Stanimirovic, I., 2008. A generalization of Fibonacci and Lucas matrices. Discrete Applied Mathematics 156, 2606–2619.
- Taher, R. B., Rachidi, M., 2003. On the matrix power and exponential by the r- generalized Fibonacci sequences methods: the companion matrix case. Linear Algebra and its Applications 370, 341–353.
- Taşçı, D., Kılıç, E., 2004. On the order-k generalized Lucas numbers. Applied Mathematics and Computation, 155, 637-641.
- Taşyurdu, Y., Gültekin, İ., 2013. On period of Fibonacci Sequences in Finite Rings with Identity of Order . Journal of Mathematics and System Science, 3(7), 349-352.
- Taşyurdu, Y., Gültekin, İ., 2016. New Trends in Mathematical Sciences. The Period of Fibonacci Sequences Over The Finite Field of Order p^2, 4 (1), 248-255.
- Wall, D. D., 1960. Fibonacci Series Modulo m. The American Mathematical Monthly 67, 525-532.
Year 2016,
Volume: 9 Issue: 1, 95 - 101, 20.06.2016
Abstract
Bu çalışmada, (Mikkawy ve Sogabe, 2010) çalışmasında tanımlanan yeni bir ailenin, { ( )} Fibonacci dizilerinin moduna göre basit periyodik diziler olduğu gösterildi. Yeni aile ve bilinen Fibonacci sayıları arasındaki bazı ilişkileri verdik. Ayrıca, yeni aile ve Lucas sayıları ile ilgili bazı teoremleri ispatladık
Keywords
References
- Arı, K., 2015. On h(x)-Lucas Quaternion Polynomials. Ars Combinatoria, 121, 291-303.
- Campbell, C. M., Campbell, P. P., 2005. The Fibonacci length of certain centro- polyhedral groups. Journal of Applied Mathematics and Computing 19, No.1-2, 231-240.
- Deveci, Ö., 2011. The Polytopic sequences in finite groups. Discrete Dynamics in Nature and Society Vol. 2011, 12 pages.
- Deveci, Ö., 2015. The Pell-padovan sequences and The Jacobsthal-Padovan seuences in finite groups. Util. Math. 98, 257-270.
- Grabowski, A., Wojtecki, P., 2004. Lucas numbers and generalized Fibonacci numbers. Form. Math. 12, 329–334.
- İpek, A., Arı, K., 2014. On Hessenberg and pentadiagonal determinants related with Fibonacci and Fibonacci-like numbers. Applied Mathematics and Computation, 229 (25), 433-439.
- İpek, A., Arı, K., 2015. On h(x)-Fibonacci octonion polynomials. Alabama Journal of Mathematics, 39.
- Kılıç, E., Tasci, D., 2006. On the Generalized Order-k Fibonacci and Lucas Numbers. Rocky Mountain Journal of Mathematics, 36, 1915-1926.
- Knox, S. W., 1992. Fibonacci Sequences In Finite groups. Fibonacci Quart., 30 No:2, 116-120.
- Lee, G. Y., 2000. k-Lucas numbers and associated bipartite graph. Linear Algebra and its Applications 320, 51–61.
- Lü, K., Wang, J., 2007. k-step Fibonacci sequence modulo m. Util. Math. 71, 169-178.
- Mikkawy, M., Sogabe, T., 2010. A new family of k-Fibonacci numbers. Applied Mathematics and Computation 215, 4456–4461.
- Stanimirovic, P. S., Nikolov J., Stanimirovic, I., 2008. A generalization of Fibonacci and Lucas matrices. Discrete Applied Mathematics 156, 2606–2619.
- Taher, R. B., Rachidi, M., 2003. On the matrix power and exponential by the r- generalized Fibonacci sequences methods: the companion matrix case. Linear Algebra and its Applications 370, 341–353.
- Taşçı, D., Kılıç, E., 2004. On the order-k generalized Lucas numbers. Applied Mathematics and Computation, 155, 637-641.
- Taşyurdu, Y., Gültekin, İ., 2013. On period of Fibonacci Sequences in Finite Rings with Identity of Order . Journal of Mathematics and System Science, 3(7), 349-352.
- Taşyurdu, Y., Gültekin, İ., 2016. New Trends in Mathematical Sciences. The Period of Fibonacci Sequences Over The Finite Field of Order p^2, 4 (1), 248-255.
- Wall, D. D., 1960. Fibonacci Series Modulo m. The American Mathematical Monthly 67, 525-532.
There are 18 citations in total.
Details
| Journal Section | Makaleler |
|---|---|
| Authors | |
| Publication Date | June 20, 2016 |
| Published in Issue | Year 2016 Volume: 9 Issue: 1 |