Tridiagonal matrices related to subsequences of balancing and Lucas-balancing numbers

Prasanta K Ray and Gopal K Panda
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 21, 2015, Number 3, Pages 56–63
Full paper (PDF, 176 Kb)

Details

Authors and affiliations

Prasanta K Ray
Department of Mathematics, Veer Surendra Sai University of Technology
Odisha, Burla-768018, India

Gopal K Panda
Department of Mathematics, National Institute of Technology Rourkela
Rourkela-769008, India

Abstract

It is well known that balancing and Lucas-balancing numbers are expressed as determinants of suitable tridiagonal matrices. The aim of this paper is to express certain subsequences of balancing and Lucas-balancing numbers in terms of determinants of tridiagonal matrices. Using these tridiagonal matrices, a factorization of the balancing numbers is also derived.

Keywords

• Balancing numbers
• Balancers
• Lucas-balancing numbers
• Tridiagonal matrices

AMS Classification

• 11B39
• 11B83

References

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