We consider gradings on cluster algebras generated by 3 x 3 skew-symmetric matrices. We show that, except in one particular case, mutation-cyclic matrices give rise to gradings in which all occurring degrees are positive and have only finitely many associated cluster variables. For mutation-acyclic matrices, we prove that all occurring degrees are associated with infinitely many variables. We also give a direct proof that the gradings are balanced in this case (i.e. that there is a bijection between the cluster variables of degree d and - d for each occurring degree d).
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