Some Classes of Tetradiagonal Determinants via Certain Polynomial Families

We present six families of tetradiagonal matrices and their periodic variations depending on four variables. We explicitly evaluate their $LU$-decompositions and determinants via certain four-parameter polynomials, some of which are called four-parameter Tribonacci and generalized Delannoy polynomials. We give generating functions for their determinant evaluations. Furthermore, we present applications of our results to some orthogonal polynomial families.