  In a recent study we considered W3 Toda 4-point functions that involve matrix
elements of a primary field with the highest-weight in the adjoint
representation of sl3. We generalize this result by considering a
semi-degenerate primary field, which has one null vector at level two. We
obtain a sixth-order Fuchsian differential equation for the conformal blocks.
We discuss the presence of multiplicities, the matrix elements and the fusion
rules.
