Generalized K-Fibonacci Sequence of Q- Matrix
Main Article Content
Abstract
This article explores the generalized K-Fibonacci sequence derived from matrices, extending the classical Fibonacci sequence to matrix representations. The properties and its applications are also described. The interplay of matrix algebra and generalized Fibonacci sequences offers insights into advanced sequence theory.
Downloads
Article Details

Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
References
T. Koshy, Fibonacei and Lucas Numbers with Applications, John Wiley & Sons, 2011.
G. Cerda-Morales, On generalized Fibonacei and Lucas numbers by matrix methods, Hacet. J. Math. Stat. 42(2) (2013), 173-179.
A. D. Godase and M. B. Dhakne, On the properties of generalized k-Fibonaccilike sequence using matrices, Indian Journal in Number Theory I (2014), 35-42.
D. Kalman, Generalized Fibonacci numbers by matrix methods, Fibonacci Quart. 20(1) (1982), 73-76.
Z. Akyuz and S. Halici, some identities deriving from the nth power of a special matrix, Advances in Difference Equations 2012(1) (2012), 223.
A. Borges, P. Catarino, A. P. Aires, P. Vasco and H. Campos, Two-by-two matrices involving k-Fibonacci and k-Lucas sequences, Appl. Math. Sci. 8(34) (2014), 1659-1666.
Henry W. Gould, A history of the Fibonacci Q-matrix and a higher-dimensional problem, Fibonacci Quart. 19(3) (1981), 250-257.
Douglas A. Lind, The Q matrix as a counterexample in group theory, Fibonacci Quart. 5 (1967), 44.
Charles H. King, Some properties of the Fibonacci numbers, Master's Thesis, San Jose State College, June 1960.
S. L. Basin and V. E. Hoggatt, Jr., A primer for the Fibonacci sequence, Part II, Fibonacci Quart. 1(2) (1963), 61-68.
J. R. Silvester, Fibonacci properties by matrix methods, The Mathematical Gazette 63(425) (1979), 188-191.
R. A. Rosenbaum, An application of matrices to linear recursion relations, Amer. Math. Monthly 66 (1959), 792-793.
E. P. Miles, Jr., Generalized Fibonacci numbers and associated matrices, Amer. Math. Monthly 67 (1960), 745-752.
J. Ivie, A general Q-matrix, Fibonacci Quart. 10(3) (1972), 255-264.
J. L. Brenner, Lucas matrix, Amer. Math. Monthly 58 (1951), 220-221.
Nasir Ahmad and Leena Prasher, Q_1 and Q_2 matrix representations of generalized k-Fibonacci sequence, JP Journal of Algebra, Number Theory and Applications 54 (2022), 19-34. http://dx.doi.org/10.17654/0972555522013
Kumar, N. K., & Sahani, S. K. (2024). Matrices of Fibonacci Numbers. Mikailalsys Journal of Mathematics and Statistics, 3(1), 71-80. https://doi.org/10.58578/mjms.v3i1.4398
Kumar, N. K. (2023). Determination of the Eigen Values of Nurlund Matrix as an operator on Sequence Spaces C and C_0. SSRN: DOI: 10.2139/ssrn.4615935
Kumar, N. K., & Sahani, S. K. (2024). Matrices of Fibonacci Numbers. Mikailalsys Journal of Mathematics and Statistics, 3(1), 71-80. https://doi.org/10.58578/mjms.v3i1.4398




















