We demonstrate how a sequence model and a sampling-based planner can influence each other to produce efficient plans and how such a model can automatically learn to take advantage of observations of the environment. Sampling-based planners such as RRT generally know nothing of their environments even if they have traversed similar spaces many times. A sequence model, such as an HMM or LSTM, guides the search for good paths. The resulting model, called DeRRT*, observes the state of the planner and the local environment to bias the next move and next planner state. The neural-network-based models avoid manual feature engineering by co-training a convolutional network which processes map features and observations from sensors. We incorporate this sequence model in a manner that combines its likelihood with the existing bias for searching large unexplored Voronoi regions. This leads to more efficient trajectories with fewer rejected samples even in difficult domains such as when escaping bug traps. This model can also be used for dimensionality reduction in multi-agent environments with dynamic obstacles. Instead of planning in a high-dimensional space that includes the configurations of the other agents, we plan in a low-dimensional subspace relying on the sequence model to bias samples using the observed behavior of the other agents. The techniques presented here are general, include both graphical models and deep learning approaches, and can be adapted to a range of planners.