  We consider an Ansatz for the study of the existence of formal integrals of
motion for Kahan-Hirota-Kimura discretizations. In this context, we give a
combinatorial proof of the formula of Celledoni-McLachlan-Owren-Quispel for an
integral of motion of the discretization in the case of cubic Hamiltonian
systems on symplectic vector spaces and Poisson vector spaces with constant
Poisson structure.
