When does Inauguration Day next fall on a Sunday?

Traditionally whenever Inauguration Day falls on Sunday the President-elect is sworn into office in private with a public ceremony on Monday. The last time this happened what with Ronald Reagan in 1981. When does it happen again?

Sunday 20 January 2013.

Nitpick: it was Reagan’s re-inauguration, in 1985, that fell on a Sunday. This makes sense because the Gregorian calendar repeats itself every 28 years (at least until 2100), so the 28-year gap between January 20s falling on Sundays is the least often it can happen.

It’s also the most frequently it can happen (at least through 2100). Inauguration day goes through this sequence:
Sun Fri Wed Mon Sat Thurs Tues
always moving two week days backwards