A categorification of cluster algebras of type B and C through symmetric quivers

We express cluster variables of type B n and C n in terms of cluster variables of type A n . Then we associate a cluster tilted bound symmetric quiver Q of type A 2 n − 1 to any seed of a cluster algebra of type B n and C n . Under this correspondence, cluster variables of type B n (resp. C n ) correspond to orthogonal (resp. symplectic) indecomposable representations of Q . We find a Caldero-Chapoton map in this setting. We also give a categorical interpretation of the cluster expansion formula in the case of acyclic quivers.