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Matrix Representation of Recursive Sequences of Order 3 and Its Applications

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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.

Scholarship

Output type

Scholarship:
Journal Article
Article
Research
 Peer-review

Original language

American English

Journal (Volume, Issue Number)

Journal of Mathematical Research with Applications (JMRA) (Volume 38)

Publication milestones

  • Published - 05/2018

Publication status

Published - 05/2018

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