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Python, 77

def f(x):
 t=0
 if x:t=f(x-1)-x;t=t+2*x*(t*(t>0)in map(f,range(x)))
 return t

Thanks to @xnor's tips on the other Python answer! (I just realised that both look very similar.)

Does anyone know of some way to reduce the number of all those spaces and tabs?

Python, 73

def f(x,t=0):
 if x:t=f(x-1);t+=2*x*(t*(t>0)in map(f,range(x)))
 return t

Edit 1: Thanks to @xnor's tips on the other Python answer! (I just realised that both look very similar.)

Edit 2: Thanks again, @xnor.

Python, 81

def f(x):                                                                 
 if x:a=f(x-1);return(a-x,a+x)[a-x in map(f,range(x))or a<=x]
 return 0

Python, 77

def f(x): 
 t=0
 if x:t=f(x-1)-x;t=t+2*x*(t*(t>0)in map(f,range(x)))
 return t

Thanks to @xnor's tips on the other Python answer! (I just realised that both look very similar.)

Does anyone know of some way to reduce the number of all those spaces and tabs?

Python (under progress)

def f(x):                                                                 
 if x:a=f(x-1);return(a+x,a-x)[a-x not in map(f,range(x)) and a>x]
 return 0

Python, 81

def f(x):                                                                 
 if x:a=f(x-1);return(a-x,a+x)[a-x in map(f,range(x))or a<=x]
 return 0