Sequences of Tridovan and their identities

Renata Passos Machado Vieira and Francisco Regis Vieira Alves
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 25, 2019, Number 3, Pages 185-197
DOI: 10.7546/nntdm.2019.25.3.185-197
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Authors and affiliations

Renata Passos Machado Vieira
Department of Mathematics
Institute Federal of Technology of the State of Ceará (IFCE)
Fortaleza-CE, Brazil

Francisco Regis Vieira Alves
Department of Mathematics
Institute Federal of Technology of the State of Ceará (IFCE)
Fortaleza-CE, Brazil


This work introduces the so-called Tridovan sequence which is an extended form of the Padovan sequence. In a general definition, this extension adds one more term to the Padovan recurrence relation, considering now the three terms preceding the penultimate one. Studies carried out on the proposed extension reveal properties of the positive and negative integer index, the sum of all, even and odd terms, the obtaining Tridovan Q-matrix and finally the Tridovan initial terms generalization.


  • Sequence of Tridovan
  • Positive indices
  • Negative indices
  • Generating matrix

2010 Mathematics Subject Classification

  • 11B37
  • 11B39


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Cite this paper

Vieira, R. P. M. & Alves, F. R. V. (2019). Sequences of Tridovan and their identities. Notes on Number Theory and Discrete Mathematics, 25(3), 185-197, doi: 10.7546/nntdm.2019.25.3.185-197.

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