Listen to 4:16 on the Return of the King complete recordings track "Shelob The Great" and at 0:21 in the track "Under Hill" from An Unexpected Journey.
Obviously it's in no relation just funny how that little bit which scores Sam thinking Frodo is dead is exactly like the main theme in the first Hobbit film.
Five notes that sound nearly identical. Nice catch. I might never have caught that myself. Of course, Thorin's theme takes a completely different direction from there, but it's still interesting to see that the seed of the idea was in Shore's mind back in 2003.
While we're at it: I found another, though less pronounced "Hobbit seed" in the Complete Recordings, this time in the track 'The Dreams of Trees' from TTT, when Treebeard talks of a shadow lying over Fangorn (from 1:33 onwards) ...
... we get something that is reminiscent of Smaug's theme (like in 'In the Shadow of the Mountain' of DOS from 1:55)
