Ömür Deveci and Anthony G. Shannon

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

Volume 23, 2017, Number 3, Pages 100–114

**Full paper (PDF, 315 Kb)**

## Details

### Authors and affiliations

Ömür Deveci

*Associate Professor, Faculty of Science and Letters
Kafkas University 36100, Turkey
*

Anthony G. Shannon

*Emeritus Professor, Faculty of Engineering & IT, University of Technology
Sydney, 2007, Australia
*

### Abstract

This paper develops properties of recurrence sequences defined from circulant matrices obtained from the characteristic polynomial of the Pell-Padovan sequence. The study of these sequences modulo m yields cyclic groups and semigroups from the generating matrices. Finally, we obtain the lengths of the periods of the extended sequences in the extended triangle groups *E*(2, *n*, 2), *E*(2, 2, *n*) and *E*(*n*, 2, 2) for *n* ≥ 3 as applications of the results obtained.

### Keywords

- Circulant matrix
- Sequence
- Group
- Length

### AMS Classification

- 11B50
- 20F05
- 11C20
- 20D60

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## Related papers

- İpek, G., Deveci, Ö.
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## Cite this paper

Deveci, Ö, & Shannon, A. G. (2017). Pell–Padovan-circulant sequences and their applications. *Notes on Number Theory and Discrete Mathematics*, 23(3), 100-114.