Research Article

Padovan and Perrin Hybrid Number Identities

Volume: 4 Number: 4 December 27, 2021
EN

Padovan and Perrin Hybrid Number Identities

Abstract

This work investigates the numbers of Padovan and Perrin hybrids. At first, the hybrid numbers, the sequences in the hybrid form, and their matrix forms are ordered as studied sequences. Thus, it was possible to display the negative index hybrids, define some identities belonging to these hybrid sequences, develop novel theorems and present them as binomial sums of the Padovan and Perrin hybrids.

Keywords

Identities, Hybrid numbers, Padovan sequence, Perrin sequence.

References

  1. [1] J. Aarts, R. Fokkink, G. Kruijtzer, Morphic numbers, Nieuw Archief voor Wiskunde, 5(2) (2001), 56-58.
  2. [2] K. Adegoke, Summation identities involving Padovan and Perrin numbers, arXiv preprint arXiv:1812.03241, (2018).
  3. [3] P. Catarino, On k-pell hybrid numbers, J. Disc. Math. Sci. Cryp., Taylor & Francis, (2019), 1-7.
  4. [4] G. Cerda-Morales, Investigation of generalized hybrid Fibonacci numbers and their properties, arXiv preprint arXiv:1806.02231, (2018).
  5. [5] R. Ferreira, N´umeros m´orficos, Dissertac¸ ˜ao de Mestrado Profissional em Matem´atica, Universidade Federal da Para´ıba, Jo˜ao Pessoa, 2015.
  6. [6] K. Khompungson, B. Rodjanadid, S. Sompong, Some matrices in term of Perrin and Padovan sequences, Thai J. Math., 17(3) (2019), 767-774.
  7. [7] M. C. dos S. Mangueira, et al., A generalizac¸ ˜ao da forma matricial da sequˆencia de Perrin, Revista Sergipana de Matem´atica e Educac¸ ˜ao Matem´atica, 5(1) (2020), 384-392.
  8. [8] M. C. dos S. Mangueira, R. P. M. Vieira, F. R. V. Alves, P. M. M. C. Catarino, The hybrid numbers of Padovan and some identities, Annales Mathematicae Silesianaei 1(ahead-of-print), Sciendo, (2020).
  9. [9] M. C. dos S. Mangueira, F. R. V. Alves, P. M. M. C. Catarino. N´umeros h´ıbridos de Mersenne, C.Q.D.-Revista Eletrˆonica Paulista de Matem´atica, 18 (2020), 1-11.
  10. [10] M. O¨ zdemir. Introducion to hybrid numbers, Adv. App. Cliff. Alg., 28 (2018).
APA
Vieira, R., Mangueira, M., Alves, F. R., & Cruz Catarino, P. M. M. (2021). Padovan and Perrin Hybrid Number Identities. Communications in Advanced Mathematical Sciences, 4(4), 190-197. https://doi.org/10.33434/cams.964042
AMA
1.Vieira R, Mangueira M, Alves FR, Cruz Catarino PMM. Padovan and Perrin Hybrid Number Identities. Communications in Advanced Mathematical Sciences. 2021;4(4):190-197. doi:10.33434/cams.964042
Chicago
Vieira, Renata, Milena Mangueira, Francisco Regis Alves, and Paula Maria Machado Cruz Catarino. 2021. “Padovan and Perrin Hybrid Number Identities”. Communications in Advanced Mathematical Sciences 4 (4): 190-97. https://doi.org/10.33434/cams.964042.
EndNote
Vieira R, Mangueira M, Alves FR, Cruz Catarino PMM (December 1, 2021) Padovan and Perrin Hybrid Number Identities. Communications in Advanced Mathematical Sciences 4 4 190–197.
IEEE
[1]R. Vieira, M. Mangueira, F. R. Alves, and P. M. M. Cruz Catarino, “Padovan and Perrin Hybrid Number Identities”, Communications in Advanced Mathematical Sciences, vol. 4, no. 4, pp. 190–197, Dec. 2021, doi: 10.33434/cams.964042.
ISNAD
Vieira, Renata - Mangueira, Milena - Alves, Francisco Regis - Cruz Catarino, Paula Maria Machado. “Padovan and Perrin Hybrid Number Identities”. Communications in Advanced Mathematical Sciences 4/4 (December 1, 2021): 190-197. https://doi.org/10.33434/cams.964042.
JAMA
1.Vieira R, Mangueira M, Alves FR, Cruz Catarino PMM. Padovan and Perrin Hybrid Number Identities. Communications in Advanced Mathematical Sciences. 2021;4:190–197.
MLA
Vieira, Renata, et al. “Padovan and Perrin Hybrid Number Identities”. Communications in Advanced Mathematical Sciences, vol. 4, no. 4, Dec. 2021, pp. 190-7, doi:10.33434/cams.964042.
Vancouver
1.Renata Vieira, Milena Mangueira, Francisco Regis Alves, Paula Maria Machado Cruz Catarino. Padovan and Perrin Hybrid Number Identities. Communications in Advanced Mathematical Sciences. 2021 Dec. 1;4(4):190-7. doi:10.33434/cams.964042

Cited By

A Note on Horadam Hybrinomials

Fundamental Journal of Mathematics and Applications

https://doi.org/10.33401/fujma.993546

Geonardo numbers

Boletim da Sociedade Paranaense de Matemática

https://doi.org/10.5269/bspm.76581