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Yıl 2021, Cilt: 4 Sayı: 4, 190 - 197, 27.12.2021

Renata Vieira Milena Mangueira Francisco Regis Alves Paula Maria Machado Cruz Catarino

https://doi.org/10.33434/cams.964042
Cited By: 1

Öz

Kaynakça

  • [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

Yıl 2021, Cilt: 4 Sayı: 4, 190 - 197, 27.12.2021

Renata Vieira Milena Mangueira Francisco Regis Alves Paula Maria Machado Cruz Catarino

https://doi.org/10.33434/cams.964042
Cited By: 1

Öz

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.

Anahtar Kelimeler

Identities Hybrid numbers Padovan sequence Perrin sequence.

Kaynakça

  • [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.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Renata Vieira

Milena Mangueira 0000-0002-4446-155X

Francisco Regis Alves 0000-0003-3710-1561

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

Yayımlanma Tarihi 27 Aralık 2021
Gönderilme Tarihi 7 Temmuz 2021
Kabul Tarihi 20 Ekim 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 4 Sayı: 4

Kaynak Göster

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. Aralık 2021;4(4):190-197. doi:10.33434/cams.964042
Chicago Vieira, Renata, Milena Mangueira, Francisco Regis Alves, ve Paula Maria Machado Cruz Catarino. “Padovan and Perrin Hybrid Number Identities”. Communications in Advanced Mathematical Sciences 4, sy. 4 (Aralık 2021): 190-97. https://doi.org/10.33434/cams.964042.
EndNote Vieira R, Mangueira M, Alves FR, Cruz Catarino PMM (01 Aralık 2021) Padovan and Perrin Hybrid Number Identities. Communications in Advanced Mathematical Sciences 4 4 190–197.
IEEE R. Vieira, M. Mangueira, F. R. Alves, ve P. M. M. Cruz Catarino, “Padovan and Perrin Hybrid Number Identities”, Communications in Advanced Mathematical Sciences, c. 4, sy. 4, ss. 190–197, 2021, doi: 10.33434/cams.964042.
ISNAD Vieira, Renata vd. “Padovan and Perrin Hybrid Number Identities”. Communications in Advanced Mathematical Sciences 4/4 (Aralık 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 vd. “Padovan and Perrin Hybrid Number Identities”. Communications in Advanced Mathematical Sciences, c. 4, sy. 4, 2021, ss. 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.

Cited By

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