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) Note also that you can split up the $n\geq 5$ case in $n=5$, which is the tame case, i.e. there is a classification of the infinitely many indecomposable modules, and the $n>5$ case, where a classification is not possible.

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) Note also that you can split up the $n\geq 5$ case in $n=5$, which is the tame case, i.e. there is a classification of the infinitely many indecomposable modules, and the $n>5$ case, where a classification is not possible.

EDIT: There is a proof in Semicanonical bases and preprojective algebras by Geiss, Leclerc, Schröer, Section 9, via the theory of Galois coverings. The Auslander-Reiten quiver of these algebras can also be found there. The statement was long before and is probably part of the folklore in the representation theory of quivers.

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)

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) Note also that you can split up the $n\geq 5$ case in $n=5$, which is the tame case, i.e. there is a classification of the infinitely many indecomposable modules, and the $n>5$ case, where a classification is not possible.