Methods and systems are provided for regenerating a lean NOx trap. In one example, a method may include, responsive to an indication to regenerate a lean NOx trap (LNT), operating an engine with an overall rich air-fuel ratio to regenerate the LNT while minimizing fuel oil dilution by operating each cylinder of the engine with an alternating rich to lean air-fuel ratio pattern of two rich combustion events for every one lean combustion event across a plurality of engine cycles.