“…[2,3] At the same time, and being already understood the connection between the 2-symmetric character with a simple cubic decomposition, for example , [4] a wide cubic decomposition was stated and developed. [5,6] As it is examined during this text, the simplest version of such decompositions, when applied to the sequence of monomials {x n } n≥0 , usually called canonical sequence, provides only trivial polynomial components. Therefore, we have considered wider versions of these decompositions, for which an interesting feature is obtained that both the quadratic and the cubic decomposition of the canonical sequence fulfil.…”