  We consider an orbit category of the bounded derived category of a path
algebra of type A_n which can be viewed as a -(m+1)-cluster category, for m >=
1. In particular, we give a characterisation of those maximal m-rigid objects
whose endomorphism algebras are connected, and then use it to explicitly study
these algebras. Specifically, we give a full description of them in terms of
quivers and relations, and relate them with (higher) cluster-tilted algebras of
type A. As a by-product, we introduce a larger class of algebras, called
'tiling algebras'.
