Generalized Fibonacci and k-Pell matrix sequences: Another way of demonstrating their properties

Francisco Regis Vieira Alves and Paula Maria Machado Cruz Catarino
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 25, 2019, Number 4, Pages 110–122
DOI: 10.7546/nntdm.2019.25.4.110-122
Full paper (PDF, 239 Kb)

Details

Authors and affiliations

Francisco Regis Vieira Alves
Department of Mathematics, Federal Institute of Science and Education of Ceara
122, 13 de Maio, Brazil

Paula Maria Machado Cruz Catarino
Department of Mathematics, Universidade de Trás-os-Montes e Alto Douro
Quinta de Prados, Portugal

Abstract

Recently Wani, Artaf, A., Badshah, V., Rathore, G. P. & Catarino introduced commutative matrices derived from the generalized Fibonacci matrix sequence and the k-Pell matrix sequence. In the present work, through the identification of certain special matrices, we can identify other forms of demonstration and also the description of commutative matrix properties for negative indices.

Keywords

• Generalized Fibonacci matrix sequence
• k-Pell matrix sequence

2010 Mathematics Subject Classification

• 11B37
• 11B39

References

1. Shannon, A. G., Horadam, A. & Anderson, P. G. (2006). The auxiliary equation associated with the plastic number. Notes on Number Theory and Discrete Mathematics. 12 (1), 1–12.
2. Wani, A. A., Badshah, V., Rathore, G. P. & Catarino, P. M. (2019). Generalized Fibonacci and k-Pell Matrix sequence, Journal of Mathematics, 51 (1), 17–28.
3. Turkmen, R. & Civciv, H. (2008). On the (s, t)-Fibonacci and Fibonacci matrix sequence, Ars Combinatoria, 87, 161–173.