  We study spherically symmetric static solutions of the most general
sixth-derivative gravity using series expansions. Specifically, we prove that
the only solutions of the complete theory (i.e., with generic coupling
constants) that possess a Frobenius expansion around the origin, $r=0$, are
necessarily regular. When restricted to specific branches of theories (i.e.,
imposing particular constraints on the coupling constants), families of
potentially singular solutions emerge. By expanding around $r=r_0 \neq 0$, we
identify solutions with black-hole horizons. Finally, we argue that, unlike in
fourth-derivative gravity, the conditions $R=0$ and $g_{tt}g_{rr}=-1$ are too
restrictive for sixth-derivative gravity solutions.
