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
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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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Cite this paper

APA

Ray, P. K., & Panda, G. K. (2015). Tridiagonal matrices related to subsequences of balancing and Lucas-balancing numbers. Notes on Number Theory and Discrete Mathematics, 21(3), 56-63.

Chicago

Ray, Prasanta Kumar, and Gopal K Panda. “Tridiagonal Matrices Related to Subsequences of Balancing and Lucas-balancing Numbers.” Notes on Number Theory and Discrete Mathematics 21, no. 3 (2015): 56-63.

MLA

Ray, Prasanta Kumar, and Gopal K Panda. “Tridiagonal Matrices Related to Subsequences of Balancing and Lucas-balancing Numbers.” Notes on Number Theory and Discrete Mathematics 21.3 (2015): 56-63. Print.

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