First your notation is wrong it is one for $n=1$, four for $n=2$, $12$ for $n=3$, $40$ for $n=4$, tame representation type for $n=5$ and wild for $n\geq 6$.
This is stated in Rigid modules over preprojective algebras by Geiss, Leclerc and Schröer, Sections 8.1-8.3. As noted in my comment a proof of the $n=5$ statement can be found in The module theoretic approach to quasi-hereditary algebras. (These are of course not the original references, I doubt that there is one original reference)