Abstract
We show that exceptional sequences in the abelian tube of rank $n$, which we
denote $\mathscr{ W}_n$, are related to exceptional sequences of type $B_n$ and
$C_n$ and to those of type $B_{n-1}$ and $C_{n-1}$. $\mathscr{W}_n$ has
$n^{n-1}$ exceptional sequences. These are in $1$-to-$n$ correspondence from
the $n^n$ "augmented" rooted labeled trees with $n$ vertices which, in turn,
are in bijection with exceptional sequences of type $B_n$ and $C_n$. By
determining the probability distribution of relative projectives in these
exceptional sequences, we show there are $(2n)!/n!$ signed exceptional
sequences in $\mathscr{W}_n$ and we show that these are in bijection with
signed exceptional sequences of type $B_{n-1}$ and $C_{n-1}$ by combining the
results of Buan-Marsh-Vatne and Igusa-Todorov.