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

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

Renata Vieira , Elen Viviani Pereira Spreafico , Francisco Regis Alves , Paula Maria Machado Cruz Catarino

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.

Keywords

Combinatorics, Perrin sequence, Polynomial sequence

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).