Unidimensional generalized Hubbard model in the high temperature limit

We explore the properties of the non-commutative Grassmann algebra to study the unidimensional Generalized Hubbard model, obtaining the analytical expressions for the first three terms in the high temperature expansion of its grand canonical partition function, with no restrictions to the constant parameters of the model. We obtain corrections to known results, in the case of half-filled band with hopping constants t=0 and X=0.