Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2024, Cilt: 7 Sayı: 2, 68 - 75
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
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.

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
Bölüm Makaleler
Yazarlar

José Chimpanzo 0009-0002-8658-5929

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

María Victoria Otero Espinar 0000-0002-0201-0523

Erken Görünüm Tarihi 30 Mart 2024
Yayımlanma Tarihi
Gönderilme Tarihi 20 Kasım 2023
Kabul Tarihi 24 Mart 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 7 Sayı: 2

Kaynak Göster

APA Chimpanzo, 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
AMA Chimpanzo J, Catarino PMMC, Otero Espinar MV. Some Identities and Generating Functions for Bidimensional Balancing and Cobalancing Sequences. Univ. J. Math. Appl. Mart 2024;7(2):68-75. doi:10.32323/ujma.1393569
Chicago Chimpanzo, 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 (Mart 2024): 68-75. https://doi.org/10.32323/ujma.1393569.
EndNote Chimpanzo J, Catarino PMMC, Otero Espinar MV (01 Mart 2024) Some Identities and Generating Functions for Bidimensional Balancing and Cobalancing Sequences. Universal Journal of Mathematics and Applications 7 2 68–75.
IEEE J. 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.
ISNAD Chimpanzo, José vd. “Some Identities and Generating Functions for Bidimensional Balancing and Cobalancing Sequences”. Universal Journal of Mathematics and Applications 7/2 (Mart 2024), 68-75. https://doi.org/10.32323/ujma.1393569.
JAMA Chimpanzo 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.
MLA Chimpanzo, 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.
Vancouver Chimpanzo 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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