Padovan sequence generalization – a study of matrix and generating function

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 26, 2020, Number 4, Pages 154—163
DOI: 10.7546/nntdm.2020.26.4.154-163
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Authors and affiliations

Renata Passos Machado Vieira
Department of Mathematics, Institute Federal of Tecnology of State of Ceara (IFCE)
Fortaleza-CE, Brazil

Francisco Regis Vieira Alves
Department of Mathematics, Institute Federal of Tecnology of State of Ceara (IFCE)
Fortaleza-CE, Brazil

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

Abstract

The Padovan sequence is a sequence similar to the Fibonacci sequence, the former being third order and the latter second. Having several applications in architecture, these numbers are directly related to plastic numbers. In this paper, the Padovan sequence is studied and investigated from the standpoint of linear algebra. With this, we will study the matrix and the generating function of the extensions of this sequence (Tridovan and Tetradovan), thus determining the generalization of this sequence.

Keywords

  • Generating function
  • Generalization
  • Generator matrix
  • Padovan sequence.

2010 Mathematics Subject Classification

  • 11B36
  • 11B39.

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Cite this paper

Vieira, R. P. M., Alves, F. R. V., & Catarino, P. M. M. C. (2020). Padovan sequence generalization – a study of matrix and generating function. Notes on Number Theory and Discrete Mathematics, 26 (4), 154-163, doi: 10.7546/nntdm.2020.26.4.154-163.

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