This song uses music from episode 'Half wit' where House plays and Patrick completes the song House never could. Apart form YouTube videos, I've not been able to find that particular music
Half Wit: House M.D. Piano - YouTube
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Half-Wit, House M.D. | Piano Tutorial + Sheet Music - YouTube
Half-Wit, House M.D. | Piano Tutorial + Sheet Music - YouTube
House, M.D. - Half-Wit Piano Theme - YouTube
House MD. Nostalgic piece Sheet music for Piano (Solo) | Musescore.com
Stream House MD Season 3 episode 15 (Half - Wit) Piano by Ahmed Algohary | Listen online for free on SoundCloud