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Matrix Representation of Recursive Sequences of Order $3$ and Its Applications
作者姓名:何天晓  Jeff H.-. LIAO  Peter J.-S. SHIUE
作者单位:Department of Mathematics, Illinois Wesleyan University, Bloomington, Illinois $61702$, USA,Department of Mathematics, Taiwan Normal University, Taipei $11677$, Taiwan, China,Department of Mathematical Sciences, University of Nevada, Las Vegas, Nevada, $89154$-$4020$, USA
摘    要:Here presented is a matrix representation of recursive number sequences of order $3$ defined by $a_n=pa_{n-1}+qa_{n-2}+ra_{n-3}$ with arbitrary initial conditions $a_0,$ $a_1=0$, and $a_2$ and their special cases of Padovan number sequence and Perrin number sequence with initial conditions $a_0=a_1=0$ and $a_2=1$ and $a_0=3$, $a_1=0$, and $a_2=2$, respectively. The matrix representation is used to construct many well known and new identities of recursive number sequences as well as Pavodan and Perrin sequences.

关 键 词:recursive  number  sequence  of  order  $3$    matrix  representation  of  recursive  number  sequences    Padovan  number  sequence    Perrin  number  sequence    Tribonacci  polynomial  sequence
收稿时间:2017/9/7 0:00:00
修稿时间:2018/1/13 0:00:00

Matrix Representation of Recursive Sequences of Order $3$ and Its Applications
Tianxiao HE,Jeff H.-. LIAO and Peter J.-S. SHIUE.Matrix Representation of Recursive Sequences of Order $3$ and Its Applications[J].Journal of Mathematical Research with Applications,2018,38(3):221-235.
Authors:Tianxiao HE  Jeff H- LIAO and Peter J-S SHIUE
Abstract:Here presented is a matrix representation of recursive number sequences of order 3 defined by a_n = pa_(n-1) + qa_(n-2) + ra_(n-3) with arbitrary initial conditions a_0, a_1 = 0, and a_2 and their special cases of Padovan number sequence and Perrin number sequence with initial conditions a_0 = a_1 = 0 and a_2 = 1 and a_0 = 3, a_1 = 0, and a_2 = 2, respectively. The matrix representation is used to construct many well known and new identities of recursive number sequences as well as Pavodan and Perrin sequences.
Keywords:recursive number sequence of order $3$    matrix representation of recursive number sequences  Padovan number sequence  Perrin number sequence  Tribonacci polynomial sequence
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