Watch the Rolling Hills online guitar lesson by Muriel Anderson from Essentials: Chet Atkins Style
You can think of these right hand patterns as three-finger banjo rolls, a technique used in bluegrass banjo playing. It's really just two arpeggios put together. The right hand plays thumb, index, middle, and then moves to adjacent strings with the same pattern: thumb, index, middle. "Rolling Hills" has some pretty chord progressions making use of open strings and using this technique throughout.