Renata Passos Machado Vieira, Francisco Regis Vieira Alves and Paula Maria Machado Cruz Catarino

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 27, 2021, Number 4, Pages 167–179

DOI: 10.7546/nntdm.2021.27.4.167-179

**Full paper (PDF, 187 Kb)**

## Details

### Authors and affiliations

Renata Passos Machado Vieira

*Department of Mathematics, Federal Institute of Education, Science and Technology of Ceara´
(IFCE) Fortaleza-CE, Brazil*

Francisco Regis Vieira Alves

*Department of Mathematics, Federal Institute of Education, Science and Technology of Ceara´
(IFCE) Fortaleza-CE, Brazil*

Paula Maria Machado Cruz Catarino

*Department of Mathematic, University of Tras-os-Montes and Alto Douro ´
Vila Real, Portugal*

### Abstract

Many papers developed so far for Padovan sequences properties and its extensions usually follow the one-dimensional approach. The presented work introduces new relations for a higher dimensional sequence, this approach is adopted for two, three and *n*-dimensional Padovan Sequence. Several mathematical properties are discussed for the first time in the present work.

### Keywords

- Relation
- Dimensional
- Padovan sequence
- Recurrent relations
- Two-dimensional.

### 2020 Mathematics Subject Classification

- 11B37
- 11B39

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## Related papers

- Vieira, R. P. M., Alves, F. R. V., & Catarino, P. M. M. C. (2023). A study of the complexification process of the (s,t)-Perrin sequence.
*Notes on Number Theory and Discrete Mathematics*, 29(1), 40-47.

## Cite this paper

Vieira, R. P. M., Alves, F. R. V., & Catarino, P. M. M. C. (2021). Relations on higher dimensional Padovan sequences. *Notes on Number Theory and Discrete Mathematics*, 27(4), 167-179, DOI: 10.7546/nntdm.2021.27.4.167-179.