A study of the complexification process of the (s,t)-Perrin sequence

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 29, 2023, Number 1, Pages 40–47
DOI: 10.7546/nntdm.2023.29.1.40-47
Full paper (PDF, 181 Kb)


Authors and affiliations

Renata Passos Machado Vieira
Department of Mathematics, Federal University of Ceará (UFC)
Fortaleza-CE, Brazil

Francisco Regis Vieira Alves
Department of Mathematics, Federal Institute of Education, Science and Technology of Ceará (IFCE)
Fortaleza-CE, Brazil

Paula Maria Machado Cruz Catarino
Department of Mathematic, University of Trás-os-Montes and Alto Douro
Vila Real, Portugal


The present article deals with the study of the generalized (s,t)-Perrin sequence in its complex process. Thus, from the one-dimensional model of the generalized (s,t)-Perrin sequence, imaginary units are inserted, starting with the insertion of unit i, called two-dimensional relations. Altogether, we have the n-dimensional relationships of the generalized (s,t)-Perrin sequence.


  • Generalization
  • Perrin sequence
  • Recurrences

2020 Mathematics Subject Classification

  • 11B37, 11B69


  1. Dişkaya, O., & Menken, H. (2022). On the (p,q)-Fibonacci N-dimensional recurrences. Bulletin of the International Mathematical Virtual Institute, 12(2), 205–212.
  2. Dişkaya, O., & Menken, H. (2019). On the (s,t)-Padovan and (s,t)-Perrin quaternions. Journal of Advanced Mathematical Studies, 12(2), 186–192.
  3. Padovan, R. (2002). Dom Hans van der Laan and the plastic number. Nexus Network Journal, 4(1), 181–193.
  4. Shannon, A., Anderson, P., & Horadam, A. (2006). Properties of Cordonnier, Perrin and van der Laan numbers. International Journal of Education in Mathematics, Science and Technology, 37(7), 825–831.
  5. Sokhuma, K. (2014). Matrices formula for Padovan and Perrin sequences. Applied Mathematical Sciences, 7(142), 7093–7096.
  6. Taş, S., & Karaduman, E. (2014). The Padovan sequences in finite groups. Chiang Mai Journal of Science, 41(9), 456–462.
  7. Vieira, R., & Alves, F. (2019). Explorando a sequência de Padovan através de investigação histórica e abordagem epistemológica. Boletim Gepem, 74, 161–169.
  8. Vieira, R., Alves, F., & Catarino, P. (2020). A historical analysis of the Padovan sequence. International Journal of Trends in Mathematics Education Research, 3(1), 8–12.
  9. Vieira, R., Alves, F., & Catarino, P. (2020). The (s,t)-Padovan Quaternions Matrix Sequence. Punjab University Journal of Mathematics, 52(11), 1–9.
  10. Vieira, R., Alves, F., & Catarino, P. (2021). Relations on higher dimensional Padovan sequences. Notes on Number Theory and Discrete Mathematics, 27(4), 167–179.
  11. Vieira, R., Mangueira, M., Alves, F., & Catarino, P. (2021). Perrin n-dimensional relations. Fundamental Journal of Mathematics and Applications, 4(2), 100–109.

Manuscript history

  • Received: 26 March 2022
  • Revised: 20 December 2022
  • Accepted: 9 February 2023
  • Online First: 14 February 2023

Copyright information

Ⓒ 2023 by the Authors.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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Cite this paper

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, DOI: 10.7546/nntdm.2023.29.1.40-47.

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