On the k-Jacobsthal numbers by matrix methods

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Published: Jun 30, 2015
Keywords:
Jacobsthal numbers Jacobsthal-Lucas numbers k-Jacobsthal numbers k-Jacobsthal-Lucas numbers Binet’s formula matrix methods

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Somnuk Srisawat
Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi
Wanna Sriprad
Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi
Oam Sthityanak
Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi

Abstract

In this paper, we define the gif.latex?k-Jacobsthal gif.latex?S-matrix and gif.latex?k-Jacobsthal gif.latex?W-matrix. After, by using this matrix representation, we obtain some identities and the Binet’s formula for gif.latex?k-Jacobsthal numbers.

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How to Cite
1.
Srisawat S, Sriprad W, Sthityanak O. On the k-Jacobsthal numbers by matrix methods. Prog Appl Sci Tech. [Internet]. 2015 Jun. 30 [cited 2024 Nov. 15];5(1):70-6. Available from: https://ph02.tci-thaijo.org/index.php/past/article/view/243207
Issue
Vol. 5 No. 1 (2015): January - June 2015
Section
Mathematics and Applied Statistics

References

H. Campos, P. Catarino, A.P. Aires, P. Vasco, and A. Borges. On Some Identities for -Jacobsthal –Lucas Number. Int Journal of Math. Analysis. 8(10) (2014): 489-494.

S. Falco´n, Plaza, A. The k-Fibonacci sequence and the Pascal 2-triangle. Chaos, Solitons & Fractals. 33 (1) (2007): 38-49.

AF. Horadam. Jacobsthal Number Representation. The Fibonacci Quarterly. 34(1) (1986): 79-83.

AF. Horadam. Jacobsthal and Pell curves. The Fibonacci Quarterly. 26(1) (1988): 79-83.

D. Jhala, K. Sisodiya, and G.P.S.Rathore, On Some Identities for k-Jacobsthal Number. Int Journal of Math. Analysis. 7(12) (2013): 551-556.

D. Kalman. Generalized Fibonacci numbers by matrix methods. The Fibonacci Quarterly. 20(1) (1982): 73-76.

E. Karaduman. An application of Fibonacci numbers in matrices. Appl. Math. and Comp. 147 (2003): 903-908.

E. Karaduman. On determinants of matrices with general Fibonacci numbers entries. Appl. Math. and Comp. 167 (2005) 670–676

F. Koken and D. Bozkurt. On The Jacobsthal Numbers by Matrix Methods. Int. J. Contemp. Math. Sciences. 3 (13) (2008): 605-614.

T. Koshy. Fibonacci and Lucas Numbers with Applications. New York: John Wiley and Sons; 2001.

Y. K. Panwar, B. Singh and V. K. Gupta. Generalized Identities Involving Common factors of generalized Fibonacci, Jacobsthal and Jacobsthal-Lucas numbers. International Journal of Analysis and Application. 3(1) (2013): 53-59.

J.R. Silvester. Fibonacci properties by matrix methods. Mathematical Gazette. 63 (1979): 188–191.

A. Stakhov. Fibonacci matrices, a generalization of the ‘Cassini formula’, and a new coding theory. Chaos, Solitons & Fractals. 30 (2006): 56-66.

M. Thongmoon. New Identities for the Even and Odd Fibonacci and Lucas Numbers. Int. J. Contemp. Math. Sciences. 4 (14) (2009): 671-676.