Hofstadter H-sequence
Haskell, 23 22 bytes



f 0=0
f n=n-f(f$f$n-1)


Simply uses the definition of the sequence. f(f$f$n-1) is equivalent to f (f (f (n-1))).

Test:

main = putStrLn . show $ map f [0..20]
-- =&gt; [0,1,1,2,3,4,4,5,5,6,7,7,8,9,10,10,11,12,13,13,14]


Thanks to Anders Kaseorg for a byte!