Factorizations of negatively subscripted balancing and Lucas-balancing numbers

Abstract

In this paper, we find some tridigonal matrices whose determinant and permanent are equal to the negatively subscripted balancing and Lucas- balancing numbers. Also using the First and second kind of Chebyshev polynomials, we obtain the factorization of these numbers.

Keywords

• Balancing numbers
• balancers
• Lucas-balancing numbers
• triangular numbers
• Tridiagonal matrices
• Determinant
• Permanent