  For a finite abelian group $(G,+)$, the constant $C(G)$ is defined to be the
smallest natural number $k$ such that any sequence in $G$ having length $k$
will have a subsequence of consecutive terms whose sum is zero. For a subset
$A\subseteq\mathbb Z_n$, the constant $C_A(n)$ is the smallest natural number
$k$ such that any sequence in $G$ having length $k$ has an $A$-weighted
zero-sum subsequence of consecutive terms. We determine the value of $C_A(n)$
for some particular weight-sets $A$.
