  For symmetric Kashiwara crystals of type $A$ and rank $e=2$, and for the
canonical basis elements that we call external, corresponding to weights on the
outer skin of the Kashiwara crystal, we construct the canonical basis elements
in a non-recursive manner. In particular, for a symmetric crystal with
$\Lambda=a \Lambda_0+a \Lambda_1$, we give formulae for the canonical basis
elements for all the $e$-regular multipartitions with defects either $k(a-k)$
or $k(a-k)+2a$, for $0 \leq k \leq a$.
