Hippocampal place cell sequences have been hypothesized to serve as diverse purposes as the induction of synaptic plasticity, formation and consolidation of long-term memories, or navigation and planning. The interrelation of sequence replay during offline states such as sleep or consummatory behaviors and online theta sequences during running and navigation is highly debated. Offline sequences are inherently 1-dimensional, whereas online sequences reverse with running direction and thus reflect the 2-dimensional topology of space, which poses a fundamental and unresolved inconsistency. Here, we propose a computational model of cornu ammonis 3 (CA3) and dentate gyrus (DG), where sensorimotor input drives the direction-dependent online sequences within CA3, and the intrahippocampal CA3-DG projections produces prospective intrinsic sequences. The model thereby suggests that sequence propagation on multiple 1-D manifolds underlies a relational code that contains stable signatures for the encoding of spatial memories and that could be used for prospective planning.