  In this paper, we study the maximal length of maximal green sequences for
quivers of type $\widetilde{\mathbf{D}}$ and $\widetilde{\mathbf{E}}$ by using
the theory of tilting mutation. We show that the maximal length does not depend
on the choice of the orientation, and determine it explicitly. Moreover, we
give a program which counts all maximal green sequences by length for a given
Dynkin/extended Dynkin quiver.
