On generalized Mersenne numbers, their interpretations and matrix generators

Paweł Ochalik, Andrzej Włoch

Abstract


In this paper we introduce generalized Mersenne numbers. We shall present some of their interpretations and matrix generators which are very useful for determining identities.

Keywords


Mersenne numbers; Fibonacci numbers; matrix generators

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References


Berge, C., Principles of Combinatorics, Academic Press, New York-London, 1971.

Civciv, H., Turkman, R., On the (s,t)-Fibonacci and Fibonacci Matrix Sequences, Ars Combin. 87 (2008), 161-173.

Ercolano, J., Matrix generator of Pell sequences, Fibonacci Quart. 17 (1) (1979), 71-77.

Kaygisiz, K., Sahin, A., Determinant and permanent of the Hessenberg matrix and Fibonacci type numbers, Gen. Math. Notes 9 (2) (2012), 32-41.

Kilic, E., On the usual Fibonacci and generalized order k-Pell sequences by Hessenberg matrices, Ars Combin. 94 (2010), 161-174.

Kilic, E., Stanica, P., A matrix approach for general higher order linear recurrence, Bull. Malays. Math. Sci. Soc. (2) 34 (1) (2011), 51-67.

Kilic, E., Tasci, D., On the generalized Fibonacci and Pell sequences by Hessenberg matrices, Ars Combin. 94 (2010) 161-174.

Sergeer, A. S., Generalized Mersenne matrices and Balonin’s conjecture, Automatic Control and Computer Sciences 48 (4) (2014), 214-220.

Solinas, J., Generalized Mersenne Numbers, Technical report CORR-39, Dept. of C. & O., University of Waterloo, 1999.

Available from http://www.carc.math.uwaterloo.ca

Włoch, A., Wołowiec-Musiał, M., Generalized Pell numbers and some relations with Fibonacci numbers, Ars Combin. 109 (2013), 391-403.

Zheng, Y., Shon, S., Exact inverse matrices of Fermat and Mersenne circulant matrix, Abstr. Appl. Anal. 2015 (2015), Article 760823, 10 pp.




DOI: http://dx.doi.org/10.17951/a.2018.72.1.69-76
Date of publication: 2018-06-25 09:04:06
Date of submission: 2018-06-24 22:36:21


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