On Computing of arbitrary positive integer powers for one type of anti-tridiagonal matrices of even order

In the [1-5] papers, Q.Yin, J.Rimas, Honglin Wu, etc, published some papers on computing of arbitrary positive integer powers for sparse matrices. In this new paper, we will derive the explicit expression of arbitrary positive integer powers for another type of symmetric anti-tridiagonal matrices of even order. This new paper will use the method of combining Chebyshev polynomials with bisymmetric matrix theory to get the explicit expression.