On a constant-diagonals matrix

In this paper, we consider a constant-diagonals matrix. The matrix was discussed in Wituła and Słota [R. Wituła, D. Słota, On computing the determinants and inverses of some special type of tridiagonal and constant-diagonals matrices, Appl. Math. Comput. 189 (1) (2007) 514–527]. The authors gave some results on determinant and the inverse of the matrix for some special cases. We give LU factorization and then compute determinant of the matrix. We determine eigenvalues of the matrix. Further we obtain some relationships between permanent of the matrix and terms of a certain recurrence relation.