Yıl 2018, Cilt 47, Sayı 3, Sayfalar 637 - 648 2018-06-01

A Two-by-Two matrix representation of a generalized Fibonacci sequence

Arfat Ahmad Wani [1] , G. P. S. Rathore [2] , V. H. Badshah [3] , Kiran Sisodiya [4]

44 113

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.

Fibonacci Sequence, Generalized Fibonacci Sequences and Matrix Methods
  • 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.
Birincil Dil en
Konular Matematik
Dergi Bölümü Matematik
Yazarlar

Yazar: Arfat Ahmad Wani

Yazar: G. P. S. Rathore

Yazar: V. H. Badshah

Yazar: Kiran Sisodiya

Bibtex @araştırma makalesi { hujms440358, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {Hacettepe Üniversitesi}, year = {2018}, volume = {47}, pages = {637 - 648}, doi = {}, title = {A Two-by-Two matrix representation of a generalized Fibonacci sequence}, key = {cite}, author = {Badshah, V. H. and Sisodiya, Kiran and Rathore, G. P. S. and Wani, Arfat Ahmad} }
APA Wani, A , Rathore, G , Badshah, V , Sisodiya, K . (2018). A Two-by-Two matrix representation of a generalized Fibonacci sequence. Hacettepe Journal of Mathematics and Statistics, 47 (3), 637-648. Retrieved from http://dergipark.gov.tr/hujms/issue/38121/440358
MLA Wani, A , Rathore, G , Badshah, V , Sisodiya, K . "A Two-by-Two matrix representation of a generalized Fibonacci sequence". Hacettepe Journal of Mathematics and Statistics 47 (2018): 637-648 <http://dergipark.gov.tr/hujms/issue/38121/440358>
Chicago Wani, A , Rathore, G , Badshah, V , Sisodiya, K . "A Two-by-Two matrix representation of a generalized Fibonacci sequence". Hacettepe Journal of Mathematics and Statistics 47 (2018): 637-648
RIS TY - JOUR T1 - A Two-by-Two matrix representation of a generalized Fibonacci sequence AU - Arfat Ahmad Wani , G. P. S. Rathore , V. H. Badshah , Kiran Sisodiya Y1 - 2018 PY - 2018 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 637 EP - 648 VL - 47 IS - 3 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2017 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics A Two-by-Two matrix representation of a generalized Fibonacci sequence %A Arfat Ahmad Wani , G. P. S. Rathore , V. H. Badshah , Kiran Sisodiya %T A Two-by-Two matrix representation of a generalized Fibonacci sequence %D 2018 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 47 %N 3 %R %U
ISNAD Wani, Arfat Ahmad , Rathore, G. P. S. , Badshah, V. H. , Sisodiya, Kiran . "A Two-by-Two matrix representation of a generalized Fibonacci sequence". Hacettepe Journal of Mathematics and Statistics 47 / 3 (Haziran 2018): 637-648.