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Erratum:

Year 2024, Volume: 7 Issue: 1, 1 - 11, 31.01.2024

Abstract

References

  • A. T. Benjamin, J. J. Quinn, Proofs the Realy Count: The art of Cominatorial Proof, American Mathematical Society (2003).
  • A. T. Benjamin, J. J. Quinn, The Fibonacci numbers-exposed more discretely, Math. Magazine, Vol.76, No.3, pp.182-192 (2003).
  • D. Garth, D. Mills, P. Mitchell, Polynomials Generated by the Fibonacci Sequence.\textbf{Journal of Integer Sequences}, v. 10, p. 1-12, 2007.
  • T. Koshy, Fibonacci and Lucas numbers with applications, Second edition, New York: Wiley-Interscience (2019).
  • E. V. P. Spreafico, Novas identidades envolvendo os numeros de Fibonacci, Lucas e Jacobsthal via ladrilhamentos, Doutorado em Matemática Aplicada, Universidade Estadual de Campinas - IME (2014).
  • I. Stewart, Tales of a neglected number, Scientific American, v. 274, p. 102-103, 1996.
  • S. J. Tedford, Combinatorial identities for the Padovan numbers, Fibonaccy Quarterly, Vol.57, No.4, pp.291-298 (2019).
  • R. P. M. Vieira, F. R. V. Alves, Propriedades das extensoes da Sequencia de Padovan, Revista Eletronica Paulista de Matematica, Vol.15, pp.24-40 (2019).
  • R. P. M. Vieira, Engenharia Didatica (ED): o caso da Generalizaçao e Complexificaçao da Sequencia de Padovan ou Cordonnier, Programa de Pos-Graduaçao em Ensino de Ciencias e Matematica, Instituto Federal de Educacao, Ciencia e Tecnologia do Estado do Ceara, Mestrado em Ensino de Ciências e Matematica (2020).
  • R. P. M. Vieira, F. R. V. Alves, P. M. M. C. Catarino, Combinatorial Interpretation of Numbers in the Generalized Padovan Sequence and Some of Its Extensions, Axioms, Vol.11, No.11, pp.1-9 (2022).
  • R. P. M. Vieira, M. C. dos S. Mangueira, F. R. V. Alves, P. M. M. C. Catarino, Perrin n-dimensional relations, Anale. Seria Informatica, Vol.4, No.2, pp.100-109 (2021).
  • R. P. M. Vieira, F. R. V. Alves, P. M. M. C. Catarino, Alternative views of some extensions of the Padovan sequence with the google colab, Anale. Seria Informatica, Vol.VVII, No.2, pp.266-273 (2019).
  • R. P. M. Vieira, F. R. V. Alves, P. M. M. C. Catarino, Sequencia matricial (s1,s2,s3)-Tridovan: aspectos históricos e propriedades, C.Q.D.-Revista Eletronica Paulista de Matematica, Vol.16, pp. 100-121 (2019).
  • N. Yilmaz, N. Taskara, Matrix Sequences in terms of Padovan and Perrin Numbers, Journal of Applied Mathematics, v.2013, pp.1-7 (2013).

Erratum: A NOTE OF THE COMBINATORIAL INTERPRETATION OF THE PERRIN AND TETRARRIN SEQUENCE

Year 2024, Volume: 7 Issue: 1, 1 - 11, 31.01.2024

Abstract

The present study carries out an investigation around the Perrin and Tetrarrin numbers, allowing a combinatorial interpretation for these sequences. Furthermore, it is possible to establish a study around the respective polynomial numbers of Perrin and Tetrarrin, using the bracelet method. With this, we have the definition of combinatorial models of these numbers, contributing to the evolution of these sequences with their respective combinatorial approaches. As a conclusion, there is a discussion of theorems referring to the combinatorial models of these sequences, allowing the study of the mathematical advancement of these numbers.

References

  • A. T. Benjamin, J. J. Quinn, Proofs the Realy Count: The art of Cominatorial Proof, American Mathematical Society (2003).
  • A. T. Benjamin, J. J. Quinn, The Fibonacci numbers-exposed more discretely, Math. Magazine, Vol.76, No.3, pp.182-192 (2003).
  • D. Garth, D. Mills, P. Mitchell, Polynomials Generated by the Fibonacci Sequence.\textbf{Journal of Integer Sequences}, v. 10, p. 1-12, 2007.
  • T. Koshy, Fibonacci and Lucas numbers with applications, Second edition, New York: Wiley-Interscience (2019).
  • E. V. P. Spreafico, Novas identidades envolvendo os numeros de Fibonacci, Lucas e Jacobsthal via ladrilhamentos, Doutorado em Matemática Aplicada, Universidade Estadual de Campinas - IME (2014).
  • I. Stewart, Tales of a neglected number, Scientific American, v. 274, p. 102-103, 1996.
  • S. J. Tedford, Combinatorial identities for the Padovan numbers, Fibonaccy Quarterly, Vol.57, No.4, pp.291-298 (2019).
  • R. P. M. Vieira, F. R. V. Alves, Propriedades das extensoes da Sequencia de Padovan, Revista Eletronica Paulista de Matematica, Vol.15, pp.24-40 (2019).
  • R. P. M. Vieira, Engenharia Didatica (ED): o caso da Generalizaçao e Complexificaçao da Sequencia de Padovan ou Cordonnier, Programa de Pos-Graduaçao em Ensino de Ciencias e Matematica, Instituto Federal de Educacao, Ciencia e Tecnologia do Estado do Ceara, Mestrado em Ensino de Ciências e Matematica (2020).
  • R. P. M. Vieira, F. R. V. Alves, P. M. M. C. Catarino, Combinatorial Interpretation of Numbers in the Generalized Padovan Sequence and Some of Its Extensions, Axioms, Vol.11, No.11, pp.1-9 (2022).
  • R. P. M. Vieira, M. C. dos S. Mangueira, F. R. V. Alves, P. M. M. C. Catarino, Perrin n-dimensional relations, Anale. Seria Informatica, Vol.4, No.2, pp.100-109 (2021).
  • R. P. M. Vieira, F. R. V. Alves, P. M. M. C. Catarino, Alternative views of some extensions of the Padovan sequence with the google colab, Anale. Seria Informatica, Vol.VVII, No.2, pp.266-273 (2019).
  • R. P. M. Vieira, F. R. V. Alves, P. M. M. C. Catarino, Sequencia matricial (s1,s2,s3)-Tridovan: aspectos históricos e propriedades, C.Q.D.-Revista Eletronica Paulista de Matematica, Vol.16, pp. 100-121 (2019).
  • N. Yilmaz, N. Taskara, Matrix Sequences in terms of Padovan and Perrin Numbers, Journal of Applied Mathematics, v.2013, pp.1-7 (2013).
There are 14 citations in total.

Details

Primary Language English
Subjects Algebra and Number Theory, Combinatorics and Discrete Mathematics (Excl. Physical Combinatorics), Pure Mathematics (Other)
Journal Section Research Article
Authors

Renata Vieira 0000-0002-1966-7097

Elen Viviani Pereira Spreafico 0000-0001-6079-2458

Francisco Regis Alves 0000-0003-3710-1561

Paula Maria Machado Cruz Catarino 0000-0001-6917-5093

Publication Date January 31, 2024
Published in Issue Year 2024 Volume: 7 Issue: 1

Cite

APA Vieira, R., Pereira Spreafico, E. V., Alves, F. R., Cruz Catarino, P. M. M. (2024). A NOTE OF THE COMBINATORIAL INTERPRETATION OF THE PERRIN AND TETRARRIN SEQUENCE. Journal of Universal Mathematics, 7(1), 1-11.
AMA Vieira R, Pereira Spreafico EV, Alves FR, Cruz Catarino PMM. A NOTE OF THE COMBINATORIAL INTERPRETATION OF THE PERRIN AND TETRARRIN SEQUENCE. JUM. January 2024;7(1):1-11.
Chicago Vieira, Renata, Elen Viviani Pereira Spreafico, Francisco Regis Alves, and Paula Maria Machado Cruz Catarino. “A NOTE OF THE COMBINATORIAL INTERPRETATION OF THE PERRIN AND TETRARRIN SEQUENCE”. Journal of Universal Mathematics 7, no. 1 (January 2024): 1-11.
EndNote Vieira R, Pereira Spreafico EV, Alves FR, Cruz Catarino PMM (January 1, 2024) A NOTE OF THE COMBINATORIAL INTERPRETATION OF THE PERRIN AND TETRARRIN SEQUENCE. Journal of Universal Mathematics 7 1 1–11.
IEEE R. Vieira, E. V. Pereira Spreafico, F. R. Alves, and P. M. M. Cruz Catarino, “A NOTE OF THE COMBINATORIAL INTERPRETATION OF THE PERRIN AND TETRARRIN SEQUENCE”, JUM, vol. 7, no. 1, pp. 1–11, 2024.
ISNAD Vieira, Renata et al. “A NOTE OF THE COMBINATORIAL INTERPRETATION OF THE PERRIN AND TETRARRIN SEQUENCE”. Journal of Universal Mathematics 7/1 (January 2024), 1-11.
JAMA Vieira R, Pereira Spreafico EV, Alves FR, Cruz Catarino PMM. A NOTE OF THE COMBINATORIAL INTERPRETATION OF THE PERRIN AND TETRARRIN SEQUENCE. JUM. 2024;7:1–11.
MLA Vieira, Renata et al. “A NOTE OF THE COMBINATORIAL INTERPRETATION OF THE PERRIN AND TETRARRIN SEQUENCE”. Journal of Universal Mathematics, vol. 7, no. 1, 2024, pp. 1-11.
Vancouver Vieira R, Pereira Spreafico EV, Alves FR, Cruz Catarino PMM. A NOTE OF THE COMBINATORIAL INTERPRETATION OF THE PERRIN AND TETRARRIN SEQUENCE. JUM. 2024;7(1):1-11.