On generalized Mersenne numbers, their interpretations and matrix generators

Paweł Ochalik; Andrzej Włoch

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2018)

  • Volume: 72, Issue: 1
  • ISSN: 0365-1029

Abstract

top
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.

How to cite

top

Paweł Ochalik, and Andrzej Włoch. "On generalized Mersenne numbers, their interpretations and matrix generators." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 72.1 (2018): null. <http://eudml.org/doc/290766>.

@article{PawełOchalik2018,
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.},
author = {Paweł Ochalik, Andrzej Włoch},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Mersenne numbers; Fibonacci numbers; matrix generators},
language = {eng},
number = {1},
pages = {null},
title = {On generalized Mersenne numbers, their interpretations and matrix generators},
url = {http://eudml.org/doc/290766},
volume = {72},
year = {2018},
}

TY - JOUR
AU - Paweł Ochalik
AU - Andrzej Włoch
TI - On generalized Mersenne numbers, their interpretations and matrix generators
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2018
VL - 72
IS - 1
SP - null
AB - 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.
LA - eng
KW - Mersenne numbers; Fibonacci numbers; matrix generators
UR - http://eudml.org/doc/290766
ER -

References

top
  1. Berge, C., Principles of Combinatorics, Academic Press, New York-London, 1971. 
  2. Civciv, H., Turkman, R., On the (s,t)-Fibonacci and Fibonacci Matrix Sequences, Ars Combin. 87 (2008), 161-173. 
  3. Ercolano, J., Matrix generator of Pell sequences, Fibonacci Quart. 17 (1) (1979), 71-77. 
  4. Kaygisiz, K., Sahin, A., Determinant and permanent of the Hessenberg matrix and Fibonacci type numbers, Gen. Math. Notes 9 (2) (2012), 32-41. 
  5. Kilic, E., On the usual Fibonacci and generalized order k-Pell sequences by Hessenberg matrices, Ars Combin. 94 (2010), 161-174. 
  6. Kilic, E., Stanica, P., A matrix approach for general higher order linear recurrence, Bull. Malays. Math. Sci. Soc. (2) 34 (1) (2011), 51-67. 
  7. Kilic, E., Tasci, D., On the generalized Fibonacci and Pell sequences by Hessenberg matrices, Ars Combin. 94 (2010) 161-174. 
  8. Sergeer, A. S., Generalized Mersenne matrices and Balonin’s conjecture, Automatic Control and Computer Sciences 48 (4) (2014), 214-220. 
  9. Solinas, J., Generalized Mersenne Numbers, Technical report CORR-39, Dept. of C. & O., University of Waterloo, 1999. 
  10. Available from http://www.carc.math.uwaterloo.ca 
  11. Włoch, A., Wołowiec-Musiał, M., Generalized Pell numbers and some relations with Fibonacci numbers, Ars Combin. 109 (2013), 391-403. 
  12. Zheng, Y., Shon, S., Exact inverse matrices of Fermat and Mersenne circulant matrix, Abstr. Appl. Anal. 2015 (2015), Article 760823, 10 pp. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.