The integer sequence \(a_{n}\) and its relationship with
Pell, Pell–Lucas and balancing numbers

Abstract. In this work we deduce some algebraic relations on integer sequence \(a_{n}\) and its relationship with Pell, Pell–Lucas and balancing numbers. Further we formulate the eigenvalues and spectral norm of the circulant matrix of \(a_{n}\) numbers.

Key words and phrases. Balancing numbers, Pell numbers, Pell–Lucas numbers, sums, perfect squares, circulant matrices and spectral norms.