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

https://doi.org/10.33434/cams.964042

Cited By: 2

https://izlik.org/JA55HF73XX

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] 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.