An Application of Hyperharmonic Numbers in Matrices

Year 2013, Volume: 42 Issue: 4 , - 1 , 01.04.2013

Mustafa Bahşi Süleyman Solak

https://izlik.org/JA95ZY63LR

Abstract

In this study, firstly we defined an n× k matrix, G(r) n,k , whose entriesconsist of hyperharmonic numbers. Then we obtained relation betweenPascal matrices and Gr n,k . Finally we calculated the determinant ofG r n,n .

Keywords

Pascal Matrix; Hyperharmonic numbers; Determinant

An Application of Hyperharmonic Numbers in Matrices

https://izlik.org/JA95ZY63LR

Abstract

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Keywords

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References

• Kalman D. Generalized Fibonacci numbers by matrix methods, Fibonacci Quarterly 20(1), 73–76, 1982.
• Er M.C. Sums of Fibonacci numbers by matrix methods, Fibonacci Quarterly 22(3), 204–207, 198 Karaduman E. An application of Fibonacci numbers in matrices, Applied Mathematics and Computation 147, 903–908, 2004.
• Tasci D. and Kilic E. On the order-k generalized Lucas numbers, Applied Mathematics and Computation 155, 637–641, 2004.
• Fu X. and Zhou X. On matrices related with Fibonacci and Lucas numbers, Applied Mathematics and Computation 200, 96–100, 2008.
• Conway, J.H. and Guy, R.K. The Book of Numbers, Springer-Verlag, New York, 1996. Benjamin, A.T., Gaebler, D. and Gaebler, R. A combinatorial approach to hyperharmonic numbers, Integers: Electron. J. Combin. Number Theory 3, 1–9, 2003.
• El-Mikkawy, M.E.A. On solving linear systems of the Pascal type, Applied Mathematics and Computation 136, 195–202, 2003.
• Lv, X.-G., Huang, T.-Z. and Ren, Z.-G. A new algorithm for linear systems of the Pascal type, Journal of Computational and Applied Mathematics 225, 309–315, 2009.