  The constant $C_A(n)$ is defined to be the smallest natural number $k$ such
that any sequence of $k$ elements in $\mathbb Z_n$ has a subsequence of
consecutive terms whose $A$-weighted sum is zero, where the weight set
$A\subseteq \mathbb Z_n\setminus \{0\}$. If $C_A(n)=k$, then a sequence in
$\mathbb Z_n$ of length $k-1$ which has no $A$-weighted zero-sum subsequence of
consecutive terms is called an $A$-extremal sequence. We characterize these
sequences for some particular weight sets.
