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We show that exceptional sequences in the abelian tube of rank $n$, which wedenote $\mathscr{ W}_n$, 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 fromthe $n^n$ "augmented" rooted labeled trees with $n$ vertices which, in turn,are in bijection with exceptional sequences of type $B_n$ and $C_n$. Bydetermining the probability distribution of relative projectives in theseexceptional sequences, we show there are $(2n)!/n!$ signed exceptionalsequences in $\mathscr{W}_n$ and we show that these are in bijection withsigned exceptional sequences of type $B_{n-1}$ and $C_{n-1}$ by combining theresults of Buan-Marsh-Vatne and Igusa-Todorov.

Rooted labeled trees and exceptional sequences of type $B_n/C_n$