Research Article
Year 2018,
Volume: 47 Issue: 3, 637 - 648, 01.06.2018
Abstract
References
- Borges, A., Catarino, P., Aires, A. P., Vasco, P. and Campos, H., Two-by-Two matrices involving k-Fibonacci and k-Lucas sequences, Applied Mathematical Sciences 8(34), 1659 1666, 2014.
- Godase, A. D. and Dhakne, M. B., On the properties of k-Fibonacci and k-Lucas numbers, Int. J. Adv. Appl. Math. and Mech 2 (1),100106, 2014.
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- Koken, F., and Bozkurt, D., On the Jacobsthal numbers by matrix methods, Int. J. Contemp. Math. Sciences 3(13), 605614, 2008.
- Bilgici, G., New generalizations of Fibonacci and Lucas sequences, Applied Mathematical Sciences, 8 (29), 14291437, 2014.
- Silvester, J. R., Properties by matrix methods, The Mathematical Gazette 63, (425), 188 191, 1979.
- Catarino, P., A note involving two-by-two matrices of k-Pell and k-Pell-Lucas sequences, International Mathematical Forum 8, (32), 15611568, 2013.
- Catarino, P., and Vasco, P., Some basic properties and a two-by-two matrix involving the k-Pell numbers, Int. Journal of Math. Analysis 7, (45), 2092215, 2013.
- Ugyun, S., and Eldogan, H., k-Jacobsthal and k-Jacobsthal Lucas matris sequences, Inter- national Mathematical Forum 11, (3), 145-154, 2016.
- Tasyurdu, Y., Cobanoglu, N., and Dilmen, Z., On the a new family of k-Fibonacci numbers, Journal of Science and Technology 9, (1), 95101, 2016.
Year 2018,
Volume: 47 Issue: 3, 637 - 648, 01.06.2018
Abstract
The Fibonacci sequence is a well-known example of second order recurrence sequence, which belongs to a particular class of recursive sequences. In this article, other generalized Fibonacci sequence is introduced and defined by $ H_{k,n+1}=2H_{k,n}+kH_{k,n-1},~n\geq1,~H_{k,0}=2,~H_{k,1}=1$ and $k$ is the positive real number. Also $n^{th}$ power of the generating matrix for this generalized Fibonacci sequence is established and some basic properties of this sequence are obtained by matrix methods.
References
- Borges, A., Catarino, P., Aires, A. P., Vasco, P. and Campos, H., Two-by-Two matrices involving k-Fibonacci and k-Lucas sequences, Applied Mathematical Sciences 8(34), 1659 1666, 2014.
- Godase, A. D. and Dhakne, M. B., On the properties of k-Fibonacci and k-Lucas numbers, Int. J. Adv. Appl. Math. and Mech 2 (1),100106, 2014.
- Horadam, A. F., Basic properties of a certain generalized sequence of numbers, Fibonacci Quarterly 3 (3), 161176, 1965.
- Demirturk, B., Fibonacci and Lucas Sums by matrix Methods, International Mathematical Forum 5(3), 99107, 2010.
- Koken, F., and Bozkurt, D., On the Jacobsthal numbers by matrix methods, Int. J. Contemp. Math. Sciences 3(13), 605614, 2008.
- Bilgici, G., New generalizations of Fibonacci and Lucas sequences, Applied Mathematical Sciences, 8 (29), 14291437, 2014.
- Silvester, J. R., Properties by matrix methods, The Mathematical Gazette 63, (425), 188 191, 1979.
- Catarino, P., A note involving two-by-two matrices of k-Pell and k-Pell-Lucas sequences, International Mathematical Forum 8, (32), 15611568, 2013.
- Catarino, P., and Vasco, P., Some basic properties and a two-by-two matrix involving the k-Pell numbers, Int. Journal of Math. Analysis 7, (45), 2092215, 2013.
- Ugyun, S., and Eldogan, H., k-Jacobsthal and k-Jacobsthal Lucas matris sequences, Inter- national Mathematical Forum 11, (3), 145-154, 2016.
- Tasyurdu, Y., Cobanoglu, N., and Dilmen, Z., On the a new family of k-Fibonacci numbers, Journal of Science and Technology 9, (1), 95101, 2016.
There are 11 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Article |
| Authors | |
| Publication Date | June 1, 2018 |
| Published in Issue | Year 2018 Volume: 47 Issue: 3 |