You are right about John liking this tune. It is in fact one part from the Ragtime piano number "Creole Belles". Without checking the recording I believe it is the third.

Then of course there is Richmond Blues/All Night Long, Back up and Push, Rubber Dolly Rag, the skipping game My Momma Told Me and undoubtedly numerous others.

You know the definition of country music: Three Chords and the Truth.