Jacobsthal-Mulatu Numbers
DOI:
https://doi.org/10.14244/lajm.v4i1.39Keywords:
Jacobsthal sequence, Jacobsthal-Lucas sequence, Mulatu sequence, generating functionsAbstract
The aim of this study is to find a sequence of Jacobsthal-type numbers, which we will denote by {JMn}n≥0 and name as the sequence of Jacobsthal-Mulatu, such that each term of the Jacobsthal-Lucas sequence, denoted by {jn}n≥0, is an average term between JMn and Jn, where {Jn}n≥0 is the classical Jacobsthal sequence. We investigated some key characteristics of the sequence of Jacobsthal-Mulatu. In this study, we present some interesting properties of these sequences of numbers explored in connection with the sequences {Jn}n≥0 and {jn}n≥0.
References
[1] Sloane NJA. The on-line encyclopedia of integer sequences. The OEIS Foundation Inc.; 2024. Available from: http://oeis.org.
[2] Aydın FT. On generalizations of the Jacobsthal sequence. Notes on number theory and discrete mathematics. 2018;24(1):120-35. DOI: https://doi.org/10.7546/nntdm.2018.24.1.120-135
[3] Koshy T. Fibonacci and Lucas Numbers with Applications. vol. 2. John Wiley & Sons; 2019. DOI: https://doi.org/10.1002/9781118742297
[4] Vajda S. Fibonacci and Lucas numbers, and the golden section: theory and applications. Courier Corporation; 2008.
[5] Lemma M. The Mulatu Numbers. Advances and Applications in Mathematical Sciences. 2011;10(4):431-40.
[6] Lemma M, Lambright J. Our brief Journey with some properties and patterns of the Mulatu Numbers. GPH-International Journal of Mathematics. 2021;4(01):23-9.
[7] Lemma M, Muche T, Atena A, Lambright J, Dolo S. The Mulatu Numbers, The Newly Celebrated Numbers of Pure Mathematics. GPH-International Journal of Mathematics. 2021;4(11):12-8.
[8] Prabowo A. On generalization of Fibonacci, Lucas and Mulatu numbers. International Journal of Quantitative Research and Modeling. 2020;1(3):112-22. DOI: https://doi.org/10.46336/ijqrm.v1i3.65
[9] Horadam AF. Jacobsthal representation numbers. The Fibonacci Quarterly. 1996;34(1):40-54. DOI: https://doi.org/10.1080/00150517.1996.12429096
[10] Horadam AF. A generalized Fibonacci sequence. The American Mathematical Monthly. 1961;68(5):455-9. DOI: https://doi.org/10.1080/00029890.1961.11989696
[11] Horadam AF. Basic properties of a certain generalized sequence of numbers. The Fibonacci Quarterly. 1965;3(3):161-76. DOI: https://doi.org/10.1080/00150517.1965.12431416
[12] Horadam AF. Generating functions for powers of a certain generalised sequence of numbers. Duke Mathematical Journal. 1965;32(3):437-46. DOI: https://doi.org/10.1215/S0012-7094-65-03244-8
[13] Cerda G. Matrix methods in Horadam sequences. Bolet´ ıns de Matem´ aticas. 2012;19(2):97-106.
[14] Catarino P, Vasco P, Campos H, Aires AP, Borges A. New families of Jacobsthal and Jacobsthal-Lucas numbers. Algebra and Discrete Mathematics. 2015;20(1).
[15] Dasdemir A. Mersene, Jacobsthal, and Jacobsthal-Lucas numbers with negative subscripts. Acta Mathematica Universitatis Comenianae. 2019;88(1):142-56.
[16] Horadam AF. Jacobsthal and Pell curves. The Fibonacci Quarterly. 1988;26(1):77-83. DOI: https://doi.org/10.1080/00150517.1988.12429664
[17] Soykan Y. Generalized Horadam-Leonardo numbers and polynomials. Asian J Adv Res Rep. 2023;17(8):128-69. DOI: https://doi.org/10.9734/ajarr/2023/v17i8511
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Élis Gardel da Costa Mesquita, Eudes Antonio Costa, Paula M.M.C. Catarino, Francisco R.V. Alves
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors may enter into separate contractual agreements for the non-exclusive distribution of the journal's published version of the work (for example, posting it in an institutional repository or publishing it in a book), with an acknowledgment of its initial publication in this journal.
