The topic of the paper is the third order rational difference (or iteration) equation \[ x_{n+1} = A + \frac{x_n^p}{x_{n-1}^q x_{n-2}^r}, \quad n \in \mathbb{N}_0. \] The authors present five theorems containing some conditions on the positive parameters \(p,q,r\) and \(A\) that assure either unboundedness of at least one solution or boundedness of all solutions.