Propergate Up Tree: Level 3

$$\begin{eqnarray*}M_3 = p'_{000} u_0 N + p'_{200} u_0^2 N N + p'_{220} (u_0^2 N) (u_0N) N + p'_{222} (u_0^2 N) (u_0^2 N) N \\ \end{eqnarray*}$$

Where p'_iii refer to the proportion of children of the fourth node along the longest path (but excluding those on the longest path).