We consider the problem of sequential recommendations, where at each step an agent proposes some slate of N distinct items to a user from a much larger catalog of size K >> N. The user has unknown preferences towards the recommendations and the agent takes sequential actions that optimise (in our case minimise) some user-related cost, with the help of Reinforcement Learning. The possible item combinations for a slate is N-over-K, an enormous number rendering value iteration methods intractable. We prove that the slate-MDP can actually be decomposed using just K item-related Q functions per state, which describe the problem in a more compact and efficient way. Based on this, we propose a novel model-free SARSA and Q-learning algorithm that performs N parallel iterations per step, without any prior user knowledge. We call this method SlateFree, i.e. free-ofslates, and we show numerically that it converges very fast to the exact optimum for arbitrary user profiles, and that it outperforms alternatives from the literature.