Year 2021,
Volume: 4 Issue: 4, 190 - 197, 27.12.2021
Renata Vieira
,
Milena Mangueira
,
Francisco Regis Alves
,
Paula Maria Machado Cruz Catarino
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).
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Jo˜ao Pessoa, 2015.
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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
Renata Vieira
,
Milena Mangueira
,
Francisco Regis Alves
,
Paula Maria Machado Cruz Catarino
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.