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

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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
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Birincil Dil en Matematik Matematik 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 = {Wani, Arfat Ahmad and Rathore, G. P. S. and Badshah, V. H. and Sisodiya, Kiran} } 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 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.