Matrix Representation of Recursive Sequences of Order 3 and Its Applications

Tian-Xiao He, Jeff H.C. Liao, Peter J.S. Shiue

Research output: Journal ArticleArticlepeer-review

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.
Original languageAmerican English
JournalJournal of Mathematical Research with Applications (JMRA)
Volume38
DOIs
StatePublished - May 2018

Keywords

  • recursive number sequence of order 3
  • matrix representation of recursive number sequences
  • Padovan number sequence
  • Perrin number sequence
  • Tribonacci polynomial sequence

Disciplines

  • Applied Mathematics
  • Mathematics

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