Article
Matrix Representation of Recursive Sequences of Order 3 and Its Applications
Journal of Mathematical Research with Applications (JMRA)
(2018)
Abstract
Here presented is a matrix representation of recursive number sequences of order 3 defined by an = pan-1 + qan-2 + ran-3 with arbitrary initial conditions a0; a1 = 0, and a2 and their special cases of Padovan number sequence and Perrin number sequence with initial conditions a0 = a1 = 0 and a2 = 1 and a0 = 3, a1 = 0, and a2 = 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
Disciplines
Publication Date
Spring May, 2018
DOI
10.3770/j.issn:2095-2651.2018.03.001
Publisher Statement
Journal of Mathematical Research with Applications (JMRA) is published by the Dalian University of Technology and the China Society for Industrial and Applied Mathematics. For more information about this journal please visit JMRA.
Citation Information
Tian-Xiao He, Jeff H.C. Liao and Peter J.S. Shiue. "Matrix Representation of Recursive Sequences of Order 3 and Its Applications" Journal of Mathematical Research with Applications (JMRA) Vol. 38 Iss. 3 (2018) p. 221 - 235 ISSN: 2095-2651 Available at: http://works.bepress.com/tian_xiao_he/102/