Öz
Kaynakça
- 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.
Öz
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.
Anahtar Kelimeler
Fibonacci Sequence Generalized Fibonacci Sequences and Matrix Methods
Kaynakça
- 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.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Matematik |
| Yazarlar | |
| Yayımlanma Tarihi | 1 Haziran 2018 |
| Yayımlandığı Sayı | Yıl 2018 Cilt: 47 Sayı: 3 |