We present a recurrent neural network memory that uses sparse coding to create a combinatoric encoding of sequential inputs. Using several examples, we show that the network can associate distant causes and effects in a discrete stochastic process, predict partially-observable higher-order sequences, and enable a DQN agent to navigate a maze by giving it memory. The network uses only biologically-plausible, local and immediate credit assignment. Memory requirements are typically one order of magnitude less than existing LSTM, GRU and autoregressive feed-forward sequence learning models. The most significant limitation of the memory is generalization to unseen input sequences. We explore this limitation by measuring next-word prediction perplexity on the Penn Treebank dataset.