Many memory models focus on encoding of sequences by excitatory recurrent synapses in region CA3 of the hippocampus. However, data and modeling suggest an alternate mechanism for encoding of sequences in which interference between theta frequency oscillations encodes the position within a sequence based on spatial arc length or time. Arc length can be coded by an oscillatory interference model that accounts for many features of the context-dependent firing properties of hippocampal neurons observed during performance of spatial memory tasks. In continuous spatial alternation, many neurons fire selectively depending on the direction of prior or future response (left or right). In contrast, in delayed non-match to position, most neurons fire selectively for task phase (sample vs. choice), with less selectivity for left versus right. These seemingly disparate results are effectively simulated by the same model, based on mechanisms similar to a model of grid cell firing in entorhinal cortex. The model also simulates forward shifting of firing over trials. Adding effects of persistent firing with reset at reward locations addresses changes in context-dependent firing with different task designs. Arc length coding could contribute to episodic encoding of trajectories as sequences of states and actions.