An Application of Hyperharmonic Numbers in Matrices

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

Abstract

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Keywords

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References

1. Kalman D. Generalized Fibonacci numbers by matrix methods, Fibonacci Quarterly 20(1), 73–76, 1982.
2. 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.
3. Tasci D. and Kilic E. On the order-k generalized Lucas numbers, Applied Mathematics and Computation 155, 637–641, 2004.
4. Fu X. and Zhou X. On matrices related with Fibonacci and Lucas numbers, Applied Mathematics and Computation 200, 96–100, 2008.
5. 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.
6. El-Mikkawy, M.E.A. On solving linear systems of the Pascal type, Applied Mathematics and Computation 136, 195–202, 2003.
7. 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.