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Year 2021, Volume: 4 Issue: 4, 190 - 197, 27.12.2021
https://doi.org/10.33434/cams.964042

Abstract

References

  • [1] J. Aarts, R. Fokkink, G. Kruijtzer, Morphic numbers, Nieuw Archief voor Wiskunde, 5(2) (2001), 56-58.
  • [2] K. Adegoke, Summation identities involving Padovan and Perrin numbers, arXiv preprint arXiv:1812.03241, (2018).
  • [3] P. Catarino, On k-pell hybrid numbers, J. Disc. Math. Sci. Cryp., Taylor & Francis, (2019), 1-7.
  • [4] G. Cerda-Morales, Investigation of generalized hybrid Fibonacci numbers and their properties, arXiv preprint arXiv:1806.02231, (2018).
  • [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] K. Khompungson, B. Rodjanadid, S. Sompong, Some matrices in term of Perrin and Padovan sequences, Thai J. Math., 17(3) (2019), 767-774.
  • [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] 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] 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] M. O¨ zdemir. Introducion to hybrid numbers, Adv. App. Cliff. Alg., 28 (2018).
  • [11] T. D. Senturk, et al. A Study on Horadam hybrid numbers, Turk. J. Math., 44(4) (2020), 1212-1221.
  • [12] K. Sokhuma, Matrices formula for Padovan and Perrin sequences, App. Math. Sci., 7(142) (2013), 7093-7096.
  • [13] I. Stewart, Tales of a neglected number, Scientific American, 274(6) (1996), 102-103, 1996.
  • [14] A. Szynal-Liana, The Horadam hybrid numbers, Discussiones Mathematicae-General Algebra and App., Sciendo, 38(1) (2018), 91-98.
  • [15] A. Szynal-Liana, I. Wloch. On Jacobsthal and Jacobsthal-Lucas hybrid numbers, In: Annales Mathematicae Silesianae, Sciendo, (2019), 276-283.
  • [16] R. Vieira, M. Mangueira, F. Alves, P. Catarino. Perrin n-dimensional relations, Fund. J. Math. App. 4(2) (2021), 100-109.
  • [17] N. Yilmaz. More identities on Fibonacci and Lucas hybrid numbersi Notes on Number Theory and Discrete Math. 27(2) (2021), 159-167.

Padovan and Perrin Hybrid Number Identities

Year 2021, Volume: 4 Issue: 4, 190 - 197, 27.12.2021
https://doi.org/10.33434/cams.964042

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.

References

  • [1] J. Aarts, R. Fokkink, G. Kruijtzer, Morphic numbers, Nieuw Archief voor Wiskunde, 5(2) (2001), 56-58.
  • [2] K. Adegoke, Summation identities involving Padovan and Perrin numbers, arXiv preprint arXiv:1812.03241, (2018).
  • [3] P. Catarino, On k-pell hybrid numbers, J. Disc. Math. Sci. Cryp., Taylor & Francis, (2019), 1-7.
  • [4] G. Cerda-Morales, Investigation of generalized hybrid Fibonacci numbers and their properties, arXiv preprint arXiv:1806.02231, (2018).
  • [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] K. Khompungson, B. Rodjanadid, S. Sompong, Some matrices in term of Perrin and Padovan sequences, Thai J. Math., 17(3) (2019), 767-774.
  • [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] 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] 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] M. O¨ zdemir. Introducion to hybrid numbers, Adv. App. Cliff. Alg., 28 (2018).
  • [11] T. D. Senturk, et al. A Study on Horadam hybrid numbers, Turk. J. Math., 44(4) (2020), 1212-1221.
  • [12] K. Sokhuma, Matrices formula for Padovan and Perrin sequences, App. Math. Sci., 7(142) (2013), 7093-7096.
  • [13] I. Stewart, Tales of a neglected number, Scientific American, 274(6) (1996), 102-103, 1996.
  • [14] A. Szynal-Liana, The Horadam hybrid numbers, Discussiones Mathematicae-General Algebra and App., Sciendo, 38(1) (2018), 91-98.
  • [15] A. Szynal-Liana, I. Wloch. On Jacobsthal and Jacobsthal-Lucas hybrid numbers, In: Annales Mathematicae Silesianae, Sciendo, (2019), 276-283.
  • [16] R. Vieira, M. Mangueira, F. Alves, P. Catarino. Perrin n-dimensional relations, Fund. J. Math. App. 4(2) (2021), 100-109.
  • [17] N. Yilmaz. More identities on Fibonacci and Lucas hybrid numbersi Notes on Number Theory and Discrete Math. 27(2) (2021), 159-167.
There are 17 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Renata Vieira

Milena Mangueira 0000-0002-4446-155X

Francisco Regis Alves 0000-0003-3710-1561

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

Publication Date December 27, 2021
Submission Date July 7, 2021
Acceptance Date October 20, 2021
Published in Issue Year 2021 Volume: 4 Issue: 4

Cite

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 Vieira R, Mangueira M, Alves FR, Cruz Catarino PMM. Padovan and Perrin Hybrid Number Identities. Communications in Advanced Mathematical Sciences. December 2021;4(4):190-197. doi:10.33434/cams.964042
Chicago Vieira, Renata, Milena Mangueira, Francisco Regis Alves, and Paula Maria Machado Cruz Catarino. “Padovan and Perrin Hybrid Number Identities”. Communications in Advanced Mathematical Sciences 4, no. 4 (December 2021): 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 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, 2021, doi: 10.33434/cams.964042.
ISNAD Vieira, Renata et al. “Padovan and Perrin Hybrid Number Identities”. Communications in Advanced Mathematical Sciences 4/4 (December 2021), 190-197. https://doi.org/10.33434/cams.964042.
JAMA 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, 2021, pp. 190-7, doi:10.33434/cams.964042.
Vancouver Vieira R, Mangueira M, Alves FR, Cruz Catarino PMM. Padovan and Perrin Hybrid Number Identities. Communications in Advanced Mathematical Sciences. 2021;4(4):190-7.

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