A. G. Shannon and C. K. Wong

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 14, 2008, Number 4, Pages 16—24

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## Details

### Authors and affiliations

A. G. Shannon

*Warrane College, University of New South Wales
PO Box 123, NSW 1465, Australia*

C. K. Wong

*Warrane College, University of New South Wales
PO Box 123, NSW 1465, Australia*

### Abstract

This paper considers some properties of the third order recursive sequence defined by the linear recurrence relation *w _{m,n} *= 2

^{m}w_{m, n−2}+

*w*

_{m, n−3},

*n*≥ 3,

*m*= 0, 1, 2, with appropriate initial conditions. The present work follows on from the case

*m*= 0 (Shannon

*et al*). Relationships with the well-known sequences of Fibonacci, Lucas and Pell are developed. The motivation for the study was to find analogous results to some of the second order classic identities such as, for example, Simson’s identity and Horadam’s Fibonacci number triples.

### Keywords

- Fibonacci
- Lucas
- Pell numbers
- Simson
- Convolutions
- Generating functions

### AMS Classification

- 11B37
- 11B39

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## Cite this paper

Shannon, A. G., & Wong, C. K. (2008). Some properties of generalized third order Pell numbers. Notes on Number Theory and Discrete Mathematics, 14(4), 16-24.