Indecomposable count for a cyclic defect block ($l(B)=e,\#\mathrm{ind}(B)=e{p}^n$)

For a split block of a group algebra with cyclic defect group of a block of order $q=p^n$ and inertial index of a block $e$, its Brauer tree algebra has $e$ simple modules and exceptional multiplicity $(q-1)/e$. Its stable Auslander–Reiten quiver is $\mathbb{Z}{A}_{q-1}/⟨{\tau }^e⟩$, giving $e(q-1)$ nonprojective indecomposables. Adding the $e$ indecomposable projectives gives $eq$ indecomposables in total.