This present paper is devoted to the study of a class of Nakayama algebras Nn(r) given by the path algebra of the equioriented quiver An subject to the nilpotency degree r for each sequence of r consecutive arrows. We show that the Nakayama algebras Nn(r) for certain pairs (n, r) can be realized as endomorphism algebras of tilting objects in the bounded derived category of coherent sheaves over a weighted projective line, or in its stable category of vector bundles. Moreover, we classify all the Nakayama algebras Nn(r) of Fuchsian type, that is, derived equivalent to the bounded derived categories of extended canonical algebras. We also provide a new way to prove the classification result on Nakayama algebras of piecewise hereditary type, which have been done by Happel–Seidel before.