From the time of its admission to the Union in 1812, until the division into multiple districts a decade later, Louisiana had only one congressional district. During that time, three people represented the state at-large.
District inactive, returned to district representation
In the 43rd Congress, Louisiana had six representatives. Five were assigned a district and one represented the state at-large. Due to an election contest for the at-large seat, it was vacant until the very last day.