Research Article
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Year 2024, , 68 - 75, 23.05.2024
https://doi.org/10.32323/ujma.1393569

Abstract

References

  • [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

Year 2024, , 68 - 75, 23.05.2024
https://doi.org/10.32323/ujma.1393569

Abstract

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.

References

  • [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.
There are 11 citations in total.

Details

Primary Language English
Subjects Algebra and Number Theory
Journal Section Articles
Authors

José Chimpanzo 0009-0002-8658-5929

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

María Victoria Otero Espinar 0000-0002-0201-0523

Early Pub Date March 30, 2024
Publication Date May 23, 2024
Submission Date November 20, 2023
Acceptance Date March 24, 2024
Published in Issue Year 2024

Cite

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. May 2024;7(2):68-75. doi:10.32323/ujma.1393569
Chicago Chimpanzo, José, Paula Maria Machado Cruz Catarino, and María Victoria Otero Espinar. “Some Identities and Generating Functions for Bidimensional Balancing and Cobalancing Sequences”. Universal Journal of Mathematics and Applications 7, no. 2 (May 2024): 68-75. https://doi.org/10.32323/ujma.1393569.
EndNote Chimpanzo J, Catarino PMMC, Otero Espinar MV (May 1, 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, and M. V. Otero Espinar, “Some Identities and Generating Functions for Bidimensional Balancing and Cobalancing Sequences”, Univ. J. Math. Appl., vol. 7, no. 2, pp. 68–75, 2024, doi: 10.32323/ujma.1393569.
ISNAD Chimpanzo, José et al. “Some Identities and Generating Functions for Bidimensional Balancing and Cobalancing Sequences”. Universal Journal of Mathematics and Applications 7/2 (May 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 et al. “Some Identities and Generating Functions for Bidimensional Balancing and Cobalancing Sequences”. Universal Journal of Mathematics and Applications, vol. 7, no. 2, 2024, pp. 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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