  Let $R$ be a polynomial ring over a field. We introduce the concept of
sequentially almost Cohen-Macaulay modules and describe the extremal rays of
the cone of local cohomology tables of finitely generated graded $R$-modules
which are sequentially almost Cohen-Macaulay, and describe some cases when the
local cohomology table of a module of dimension 3 has a nontrivial
decomposition.
