A West Wing question

Undoubedly this is one of the most trivial questions ever asked here. But I was watching last week’s episode of The West Wing, which featured a return appearance by John Goodman, and I was wondering how Walken’s brief Presidency affected the numbering of the Presidents. Does Walken count as the 43rd President (or whatever he’d be in the WW world)? Does Jed Bartlet now count as the 42nd and 44th President (like Cleveland did for his seperate administrations)?