On some new generalized structure of Fibonacci numbers
Resumen
Various structures of Fibonacci numbers, Bronze numbers have been studied. The main structure of this paper is to introduce a
new sequence of Gaussian Bronze Fibonacci (GBF) numbers. Some basic properties will be studied concerning it. Also, we will establish the
generalized Binet formula.
Descargas
Citas
J. J. Bravo, J. L. Herrera and F. Luca, Common values of generalized Fibonacci and Pell sequences, Journal of Number Theory 226, 51-71, (2021).
A. H. Ganie, Nature of Phyllotaxy and Topology of H-matrix, IntechOpen (Matrix Theory-Applications and Theorems), 75-86, (2018).
O. Deveci and G. Artun, On the Adjacency-Jacobsthal numbers, Communications in Algebra 47(11), 4520-4532, (2019).
P. Catarino, H. Campos and P. Vasco, A note on k-pell, k-pell-lucas and modified k-pell numbers with arithmetic indexes, Acta Mathematica Universitatis Comenianae 89(1), 97-107, (2019).
A. H. Ganie and Afroza, New type of difference sequence space of Fibonacci numbers, SciFed Computer Science & Applications 1(2), 1-7, (2018).
A. H. Ganie and A. M. Albaidan, Matrix structure of Jacobsthal numbers, Journal of Function Spaces, Volume 2021, Article ID 2888840, 5 pages.
A. H. Ganie and I. A. Dar, Extremal Problems of Bernstein-Type and an Operator Preserving Inequalities between Polynomials, Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) 59, 380-386, (2024).
A. H. Ganie, N. A. Sheikh, M. Ahmad, Taste of Matrix Methods, Scholars’ Press, 344 pages, (2017).
A. H. Ganie, E. Ozkan, M. Uysal and A. Akhter, On new polynomial sequences constructed to each vertex in an n-Gon, Discrete Dynamics in Nature and Society, Article ID 2910678, 1- 13, (2022).
M. Ddamulira and F. Luca, On the problem of Pillai with k-generalized Fibonacci numbers and powers of 3, International Journal of Number Theory 16(07), 1643-1666, (2020).
D. Kalman, Generalized Fibonacci numbers by matrix methods, Fibonacci Quartterly 20(1), 73-76, (1982).
N. Karaaslan, A note on modified Pell polynomials, Aksaray University Journal of Science and Engineering, 3(1), 1-7, (2019).
M. Khan, A. G. Hamid, On the characteristic polynomial and energy of Hermitian quasi-Laplacian matrix of mixed graphs, Asian-European Journal of Mathematics 16 (07), 2350116, (2023).
C. Levesque, On the mth-Order linear recurrences, Fibonacci Quarterly 23(4), 290-293, (1985).
J. H. Jordan, Gaussian Fibonacci and Lucas numbers, Fibonacci Quarterly 3, 315-318, (1965).
A. F. Horadam, Complex Fibonacci numbers and Fibonacci quaternions, American Math. Monthly 70, 289-291, (1963).
A. F. Horadam, A Generelized Fibonacci Sequences, American Math. Monthly 68, 455-459, (1961).
G. Berzenyi, Gaussian Fibonacci numbers, Fibonacci Quarterly 15, 233-236, (1977).
E. Ozkan, M. Ta¸stan, A. Akta¸s, On the new families of k-Pell numbers and k-Pell Lucas numbers and their polynomials, Journal of Contemporary Applied Mathematics 11(1), 16-30, (2021).
E. Ozkan and M. Ta¸stan, A new families of Gauss k-Jacobsthal numbers and Gauss k-Jacobsthal-Lucas numbers and their polynomials, Journal of Science and Arts 4(53), 893-908, (2020).
E. Ozkan and B. Kuloˇglu, On A Jacobsthal-Like Sequence Associated with KJacobsthal-Lucas Sequence, Journal of Contemporary Applied Mathematics 10(2), 3-13, (2020).
E. Ozkan, A. Aydoˇgdu and I. Altun, Some identities for a family of Fibonacci and Lucas numbers, Journal of Mathematics and Statistical Science 3(10), 295-303, (2017).
S. Pethe, and A. F. Horadam, Generalized Gaussian Fibonacci numbers, Bull. Austral. Math. Soc. 33(1), 37-48, (1986).
J. R. Silvester, Fibonacci properties by matrix methods, Mathematical Gazette 63, 188-191, (1979).
M. C. Er, Sums of Fibonacci numbers by matrix methods, The Fibonacci Quarterly 22(3), 204-207, (1984).
M. Asci and E. Gurel, Gaussian Jacobsthal and Gaussian Jacobsthal Lucas polynomials, Notes on Number Theory and Discrete Mathematics 19(1), 25-36, (2013).
R. Schneider, Fibonacci Numbers and the Golden Ratio, Parabola 52(3), 1-6, (2016).
T. A, Tarray, P. A. Naik, R. A. Nijar, Matrix Representation of an All-inclusive Fibonacci Sequence, Asian Journal of Mathematics & Statistics 11(1), 1-11, (2018).
T. Ya˘gmur, Gaussian Pell-Lucas Polynomials, Communications in Mathematics and Applications 10(4), 673-679, (2019).
Derechos de autor 2025 Boletim da Sociedade Paranaense de Matemática

Esta obra está bajo licencia internacional Creative Commons Reconocimiento 4.0.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).