何天晓,Jeff H.-. LIAO,Peter J.-S. SHIUE.Matrix Representation of Recursive Sequences of Order $3$ and Its Applications[J].数学研究及应用,2018,38(3):221~235 |
Matrix Representation of Recursive Sequences of Order $3$ and Its Applications |
Matrix Representation of Recursive Sequences of Order $3$ and Its Applications |
投稿时间:2017-09-07 修订日期:2018-01-13 |
DOI:10.3770/j.issn:2095-2651.2018.03.001 |
中文关键词: recursive number sequence of order $3$ matrix representation of recursive number sequences Padovan number sequence Perrin number sequence Tribonacci polynomial sequence |
英文关键词:recursive number sequence of order $3$ matrix representation of recursive number sequences Padovan number sequence Perrin number sequence Tribonacci polynomial sequence |
基金项目: |
作者 | 单位 | 何天晓 | Department of Mathematics, Illinois Wesleyan University, Bloomington, Illinois $61702$, USA | Jeff H.-. LIAO | Department of Mathematics, Taiwan Normal University, Taipei $11677$, Taiwan, China | Peter J.-S. SHIUE | Department of Mathematical Sciences, University of Nevada, Las Vegas, Nevada, $89154$-$4020$, USA |
|
摘要点击次数: 1749 |
全文下载次数: 1859 |
中文摘要: |
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. |
英文摘要: |
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. |
查看全文 查看/发表评论 下载PDF阅读器 |
|
|
|