  Let $\mathscr{S}$ denote the set of integer partitions into parts that differ
by at least $3$, with the added constraint that no two consecutive multiples of
$3$ occur as parts. We derive trivariate generating functions of
Andrews--Gordon type for partitions in $\mathscr{S}$ with both the number of
parts and the number of even parts counted. In particular, we provide an
analytic counterpart of Andrews' recent refinement of the Alladi--Schur
theorem.
