  Monte Carlo simulations are used to compute the centrality dependence of the
odd moments of the initial eccentricity $\epsilon_{n+1}$, relative to the even
order (n) participant planes $\Psi^*_n$ in Au+Au collisions. The results
obtained for two models of the eccentricity -- the Glauber and the factorized
Kharzeev-Levin-Nardi (fKLN) models -- indicate magnitudes which are essentially
zero. They suggest that a possible correlation between the orientations of the
the odd and even participant planes ($\Psi^*_{n+1}$ and $\Psi^*_n$
respectively), do not have a significant influence on the calculated
eccentricities. An experimental verification test for correlations between the
orientations of the the odd and even participant planes is also proposed.
