Bidimensional extensions of balancing and Lucas-balancing numbers
*J. ChimpanzoCorresponding authorjalchimpanzo@gmail.comDepartment of Exact SciencesHigher Polytechnic Institute of SoyoSoyo, Zaire-Angola, AngolaView full profile → , P. Catarinopcatarin@utad.ptDepartment of MathematicsQuinta de PradosUniversity of Trás-os-Montes e Alto DouroVila Real, 5001-801, PortugalView full profile → , P. Vascopvasco@utad.ptDepartment of MathematicsQuinta de PradosUniversity of Trás-os-Montes e Alto DouroVila Real, 5001-801, PortugalView full profile → , A. Borgesaborges@utad.ptDepartment of MathematicsQuinta de PradosUniversity of Trás-os-Montes e Alto DouroVila Real, 5001-801, PortugalView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 10 Aug 2021
- Published Online:
- 24 Jan 2024
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-1574
- Pages:
- 95–115
Abstract
Keywords
Subject Classifications
References
[1] Behera, A., and Panda, G.K., On the square roots of triangular numbers, Fibonacci Quart. 37(2) (1999), 98-105.
[2] Bezerra, F.H.C., Alves, F.R.V., and Vieira, R.P.M., Relações recorrentes bidimensionais e tridimensionais de Narayana. C.Q.D-Revista Eletrônica Paulista de Matemática, Bauru 18 (2020), 12-28. Edição Iniciação Cientfica.
[3] Catarino, P., On k–Pell hybrid numbers. J. Discrete Math. Sci. Cryptogr. 22(1) (2019), 83-89.
[4] Catarino, P., Bicomplex k–Pell Quaternions. Computational Methods and Function Theory 19(1) (2019), 65-76.
[5] Catarino, P., and Borges, A., On Leonardo numbers. Acta Mathematica Universitatis Comenianae 89(1) (2019), 75-86.
[6] Catarino, P., and Borges, A., A note on incomplete Leonardo numbers. Integers 20 (2020), 1-7, A43.
[7] Catarino, P., Campos, H., and Vasco, P., On some identities for balancing and cobalancing numbers. Annales Mathematicae et Informaticae 45 (2015), 11-24.
[8] Catarino, P., and Vasco, P., The Generalized order –m(k–Pell) numbers. Analele Stiintifice ale Universitatii Al I Cuza din Iasi - Matematica 20(1) (2020), 55-65.
[9] Karakas, A.M., and Karakas, M., A new BK–space defined by regular matrix of Lucas numbers. J. Interdiscip. Math. 22(6) (2019), 837-847.
[10] Karataş, A., and Halici, S., Some properties of bicomplex Pell and Pell-Lucas numbers. J. Inf. Optim. Sci. 42(3) (2021), 701-709.
[11] Keskin, R., and Karaatly, O., Some new properties of balancing numbers and square triangular numbers. J. Integer Seq. 15(1) (2012), Article 12.1.4.
[12] Kizilates, C., A new generalization of Fibonacci hybrid and Lucas hybrid numbers. Chaos Solitons Fractals 130 (2020), 109449, 5pp.
[13] Koshy, T., Fibonacci and Lucas Numbers with Applications, Wiley-Interscience, New York, 2001.
[14] Levesque, C., On m–th order linear recurrences. Fibonacci Quart., 23(4) (1985), 290-293.
[15] Oliveira, R.R.de, and Alves, F.R.V., Os números Gaussianos de Fibonacci e relações recorrentes bidimensionais. Revista Thema, 16(4) (2019), 745-754.
[16] Oliveira, R.R.de, Alves, F.R.V., and Paiva, R.E.B., Identidades bi e tridimensionais para os números de Fibonacci na forma complexa. C.Q.D-Revista Eletrônica Paulista de Matemática 11 (2017), 91-106. Edição Iniciação Cientfica.
[17] Panda, G.K., Sequence balancing and cobalancing numbers. Fibonacci Quart. 45(3) (2007), 265-271.
[18] Qi, F., Determinantal expressions and recurrence relations for Fubini and Eulerian polynomials. J. Interdiscip. Math. 22(3) (2019), 317-335.
[19] Vieira, R.P.M., Alves, F.R.V., and Catarino, P.M.C.C., Relações bidimensionais e identidades da sequência de Leonardo. Revista Sergipana de Matemática e Educação Matemática 2 (2019), 156-173.




