令x=1,y=0
得：4f(1)f(0)=2f(1)
f(0)=2*1/4=1/2
令 y=1
得 f(x)=f(x+1)+f(x-1)
f(x-1)=f(x)+f(x-2)
上面2式相加得 f(x+1)+f(x-2)=0
f(x-2)+f(x-5)=0
式子“f(x+1)+f(x-2)=0” 减掉“f(x-2)+f(x-5)=0”得
f(x+1)=f(x-5)
f(x)周期为6
f(2010)=f(6*335)=f(0)=1/2