Some Identities of the Modified (s,t) Jacobsthal and Modified (s,t) Jacobsthal – Lucas Numbers by the Matrix Method
Abstract
In this paper, we study the modified Jacobsthal and modified Jacobsthal – Lucas numbers, and we define the 2 x 2 matrices , and , which satisfies the relation and . Moreover, we prove some identities of modified Jacobsthal and modified Jacobsthal – Lucas numbers, some identities of the relation between modified Jacobsthal and modified Jacobsthal – Lucas numbers and some sum formulas for modified Jacobsthal and modified Jacobsthal – Lucas numbers by using these matrices.Keywords : modified Jacobsthal number ; modified Jacobsthal – Lucas number ; matrix method ; Binet’s formulasReferences
Clarke, J.H. & Shannon, A.G. (1985). Some Generalized Lucas Sequences. The Fibonacci Quarterly, 23(2), 120 – 125.
Horadam, A. F. (1961). A Generalized Fibonacci Sequence. The American Mathematical Monthly, 68(5),
455– 459.
Horadam, A. F. (1996). Jacobsthal Representation Numbers. The Fibonacci Quarterly, 34(1), 40 – 54.
Koken, F. & Bozkurt, D. (2008). On the Jacobsthal Numbers by Matrix Methods. Internation Journal of Contemporary Mathematical Sciences, 3(13), 605 – 614.
Rabago, J. F. T. (2014). Some new properties of modified Jacobsthal and Jacobsthal– Lucas numbers.
In Proceedings of the 3rd International Conference on Mathematical Sciences. (pp. 805-818).
New York: AIP.
Rabago, J. F. T. (2015). More new properties of modified Jacobsthal and Jacobsthal-Lucas numbers. Notes on Number Theory and Discrete Mathematics, 21(2), 43 – 54.
Horadam, A. F. (1961). A Generalized Fibonacci Sequence. The American Mathematical Monthly, 68(5),
455– 459.
Horadam, A. F. (1996). Jacobsthal Representation Numbers. The Fibonacci Quarterly, 34(1), 40 – 54.
Koken, F. & Bozkurt, D. (2008). On the Jacobsthal Numbers by Matrix Methods. Internation Journal of Contemporary Mathematical Sciences, 3(13), 605 – 614.
Rabago, J. F. T. (2014). Some new properties of modified Jacobsthal and Jacobsthal– Lucas numbers.
In Proceedings of the 3rd International Conference on Mathematical Sciences. (pp. 805-818).
New York: AIP.
Rabago, J. F. T. (2015). More new properties of modified Jacobsthal and Jacobsthal-Lucas numbers. Notes on Number Theory and Discrete Mathematics, 21(2), 43 – 54.
Downloads
Published
2022-01-24
Issue
Section
Research Article
