Some Identities and Generating Functions for Bidimensional Balancing and Cobalancing Sequences

Yıl 2024, Cilt: 7 Sayı: 2, 68 – 75, 23.05.2024

José Chimpanzo , Paula Maria Machado Cruz Catarino , María Victoria Otero Espinar

https://doi.org/10.32323/ujma.1393569

Öz

Kaynakça

  • [1] G. K. Gözeri, On Pell, Pell-Lucas, and balancing numbers, J. Inequal. Appl., 3 (2018). https://doi.org/10.1186/s13660-017-1599-1
  • [2] B. K. Patel, N. Irmak, P. K. Ray, A. Zaharescu, Incomplete balancing and Lucas-balancing numbers, Math. Rep. (Bucur.), 20(1) (2018), 59-72.
  • [3] G. K. Panda, T. Komatsu, R. K. Davala, Reciprocal sums of sequences involving balancing and Lucas-balancing numbers, Math. Rep. (Bucur.), 20(2) (2018), 201-214.
  • [4] C. Levesque, On m-th order linear recurrences, Fibonacci Quart., 23(4) (1985), 290–293.
  • [5] M. Vieira, V. Alves, P. Catarino, Relacoes bidimensionais e identidades da sequˆencia de Leonardo, ReviSeM, 2 (2019), 156–173. https://doi.org/10.34179/revisem.v4i2.11863
  • [6] C. Bezerra, V. Alves, M. Vieira, Relacoes recorrentes bidimensionais e tridimensionais de Narayana, C.Q.D-Revista Eletronica Paulista de Matem´atica, 18 (2020), 12–28. https://doi.org/10.21167/cqdvol18ic202023169664fhcbfrva1228
  • [7] R. R. de Oliveira, V. Alves, B. Paiva, Identidades bi e tridimensionais para os n´umeros de Fibonacci na forma complexa, C.Q.D-Revista Eletronica Paulista de Matem´atica, 11 (2017), 91–106. https://doi.org/10.21167/cqdvol11ic201723169664rrofrvarebp91106
  • [8] R. R. de Oliveira, V. Alves, Os n´umeros gaussianos de Fibonacci e relac¸ ˜oes recorrentes bidimensionais, Revista Thema, 16(4) (2019), 745–754. http://dx.doi.org/10.15536/thema.V16.2019.745-754.1333
  • [9] J. Chimpanzo, P. Catarino, P. Vasco, A. Borges, Bidimensional extensions of balancing and Lucas-balancing numbers, J. Discrete Math. Sci. Cryptogr., 27(1) (2024), 95–115.
  • [10] J. Chimpanzo, M. V. Otero-Espinar, A. Borges, P. Vasco, P. Catarino, Bidimensional extensions of cobalancing and Lucas-cobalancing numbers, Ann. Math. Sil., (2023), https://doi.org/10.2478/amsil-2023-0022
  • [11] P. Catarino, H. Campos, P. Vasco, On some identities for balancing and cobalancing numbers, Ann. Math. Inform., 45 (2015), 11–24.

Some Identities and Generating Functions for Bidimensional Balancing and Cobalancing Sequences

Yıl 2024, Cilt: 7 Sayı: 2, 68 – 75, 23.05.2024

José Chimpanzo , Paula Maria Machado Cruz Catarino , María Victoria Otero Espinar

https://doi.org/10.32323/ujma.1393569

Öz

This article studies the bidimensional versions of four number sequences: balancing, Lucas-balancing, Lucas-cobalancing and cobalancing. Some of the identities and generating functions were presented.

Anahtar Kelimeler

Bidimensional balancing, Bidimensional cobalancing, Bidimensional Lucas-balancing, Bidimensional Lucas-cobalancing, Generating functions, Some identities

Kaynakça

  • [1] G. K. Gözeri, On Pell, Pell-Lucas, and balancing numbers, J. Inequal. Appl., 3 (2018). https://doi.org/10.1186/s13660-017-1599-1
  • [2] B. K. Patel, N. Irmak, P. K. Ray, A. Zaharescu, Incomplete balancing and Lucas-balancing numbers, Math. Rep. (Bucur.), 20(1) (2018), 59-72.
  • [3] G. K. Panda, T. Komatsu, R. K. Davala, Reciprocal sums of sequences involving balancing and Lucas-balancing numbers, Math. Rep. (Bucur.), 20(2) (2018), 201-214.
  • [4] C. Levesque, On m-th order linear recurrences, Fibonacci Quart., 23(4) (1985), 290–293.
  • [5] M. Vieira, V. Alves, P. Catarino, Relacoes bidimensionais e identidades da sequˆencia de Leonardo, ReviSeM, 2 (2019), 156–173. https://doi.org/10.34179/revisem.v4i2.11863
  • [6] C. Bezerra, V. Alves, M. Vieira, Relacoes recorrentes bidimensionais e tridimensionais de Narayana, C.Q.D-Revista Eletronica Paulista de Matem´atica, 18 (2020), 12–28. https://doi.org/10.21167/cqdvol18ic202023169664fhcbfrva1228
  • [7] R. R. de Oliveira, V. Alves, B. Paiva, Identidades bi e tridimensionais para os n´umeros de Fibonacci na forma complexa, C.Q.D-Revista Eletronica Paulista de Matem´atica, 11 (2017), 91–106. https://doi.org/10.21167/cqdvol11ic201723169664rrofrvarebp91106
  • [8] R. R. de Oliveira, V. Alves, Os n´umeros gaussianos de Fibonacci e relac¸ ˜oes recorrentes bidimensionais, Revista Thema, 16(4) (2019), 745–754. http://dx.doi.org/10.15536/thema.V16.2019.745-754.1333
  • [9] J. Chimpanzo, P. Catarino, P. Vasco, A. Borges, Bidimensional extensions of balancing and Lucas-balancing numbers, J. Discrete Math. Sci. Cryptogr., 27(1) (2024), 95–115.
  • [10] J. Chimpanzo, M. V. Otero-Espinar, A. Borges, P. Vasco, P. Catarino, Bidimensional extensions of cobalancing and Lucas-cobalancing numbers, Ann. Math. Sil., (2023), https://doi.org/10.2478/amsil-2023-0022
  • [11] P. Catarino, H. Campos, P. Vasco, On some identities for balancing and cobalancing numbers, Ann. Math. Inform., 45 (2015), 11–24.

Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Cebir ve Sayı Teorisi
BölümMakaleler
Yazarlar

José Chimpanzo Higher Polytechnic Institute of Soyo 0009-0002-8658-5929 Portugal

Paula Maria Machado Cruz Catarino University of Trás-os-Montes e Alto Douro 0000-0001-6917-5093 Portugal

María Victoria Otero Espinar University of Santiago de Compostela 0000-0002-0201-0523 Spain

Erken Görünüm Tarihi30 Mart 2024
Yayımlanma Tarihi23 Mayıs 2024
Gönderilme Tarihi20 Kasım 2023
Kabul Tarihi24 Mart 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 7 Sayı: 2

Kaynak Göster

APAChimpanzo, J., Catarino, P. M. M. C., & Otero Espinar, M. V. (2024). Some Identities and Generating Functions for Bidimensional Balancing and Cobalancing Sequences. Universal Journal of Mathematics and Applications, 7(2), 68-75. https://doi.org/10.32323/ujma.1393569
AMAChimpanzo J, Catarino PMMC, Otero Espinar MV. Some Identities and Generating Functions for Bidimensional Balancing and Cobalancing Sequences. Univ. J. Math. Appl. Mayıs 2024;7(2):68-75. doi:10.32323/ujma.1393569
ChicagoChimpanzo, José, Paula Maria Machado Cruz Catarino, ve María Victoria Otero Espinar. “Some Identities and Generating Functions for Bidimensional Balancing and Cobalancing Sequences”. Universal Journal of Mathematics and Applications 7, sy. 2 (Mayıs 2024): 68-75. https://doi.org/10.32323/ujma.1393569.
EndNoteChimpanzo J, Catarino PMMC, Otero Espinar MV (01 Mayıs 2024) Some Identities and Generating Functions for Bidimensional Balancing and Cobalancing Sequences. Universal Journal of Mathematics and Applications 7 2 68–75.
IEEEJ. Chimpanzo, P. M. M. C. Catarino, ve M. V. Otero Espinar, “Some Identities and Generating Functions for Bidimensional Balancing and Cobalancing Sequences”, Univ. J. Math. Appl., c. 7, sy. 2, ss. 68–75, 2024, doi: 10.32323/ujma.1393569.
ISNADChimpanzo, José vd. “Some Identities and Generating Functions for Bidimensional Balancing and Cobalancing Sequences”. Universal Journal of Mathematics and Applications 7/2 (Mayıs 2024), 68-75. https://doi.org/10.32323/ujma.1393569.
JAMAChimpanzo J, Catarino PMMC, Otero Espinar MV. Some Identities and Generating Functions for Bidimensional Balancing and Cobalancing Sequences. Univ. J. Math. Appl. 2024;7:68–75.
MLAChimpanzo, José vd. “Some Identities and Generating Functions for Bidimensional Balancing and Cobalancing Sequences”. Universal Journal of Mathematics and Applications, c. 7, sy. 2, 2024, ss. 68-75, doi:10.32323/ujma.1393569.
VancouverChimpanzo J, Catarino PMMC, Otero Espinar MV. Some Identities and Generating Functions for Bidimensional Balancing and Cobalancing Sequences. Univ. J. Math. Appl. 2024;7(2):68-75.

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