# “Solution” of finite cluster algebras

Consider the cluster algebras $$A_n$$ and $$D_n$$. Choose any cluster $$x$$, is there an explicit formula that express all other cluster variables in terms of $$x$$?

There is a formula for the Laurent expansions of cluster variables in terms of matchings in "snake graphs" for cluster algebras from any surface. For the question type $$A$$ (a disk with marked points on the boundary) and type $$D$$ (a once punctured disk with marked points on the boundary) come from surfaces.
Edit addition: I originally thought of the more general results for surfaces given above. However, if you are particularly interested in the type $$A$$ Propp's The combinatorics of frieze patterns and Markoff numbers and Schiffler's A cluster expansion formula (An case) are very nice precursors to the above more general theorems.