Sequential recommendation aims to identify and recommend the next few items for a user that the user is most likely to purchase/review, given the user's purchase/rating trajectories. It becomes an effective tool to help users select favorite items from a variety of options. In this manuscript, we developed hybrid associations models ($\mathop {\mathtt {HAM}}\limits$) to generate sequential recommendations using three factors: 1) users’ long-term preferences, 2) sequential, high-order and low-order association patterns in the users’ most recent purchases/ratings, and 3) synergies among those items. $\mathop {\mathtt {HAM}}\limits$ uses simplistic pooling to represent a set of items in the associations, and element-wise product to represent item synergies of arbitrary orders. We compared $\mathop {\mathtt {HAM}}\limits$ models with the most recent, state-of-the-art methods on six public benchmark datasets in three different experimental settings. Our experimental results demonstrate that $\mathop {\mathtt {HAM}}\limits$ models significantly outperform the state of the art in all the experimental settings. with an improvement as much as 46.6 percent. In addition, our run-time performance comparison in testing demonstrates that $\mathop {\mathtt {HAM}}\limits$ models are much more efficient than the state-of-the-art methods. and are able to achieve significant speedup as much as 139.7 folds.