Chebyshev polynomials via quadratic and cubic decompositions of the canonical sequence

In this paper we give general quadratic and cubic decompositions of the sequence of monomials {x(n)}(n >= 0) and prove how the correspondent component sequences are connected with Chebyshev polynomial sequences (PSs). The two-way street that joins together the polynomial sequences brought by quadratic or cubic decomposition and those famous PSs is established by the reversed polynomials and initial perturbations. In the cubic decomposition case, the relation is given through a 2-orthogonal Chebyshev PS.