对所有非负整数都有f(x)=f(x-1)+f(x+1)且f(0)=2004`求f(2004)

对所有非负整数都有f(x)=f(x-1)+f(x+1)且f(0)=2004`求f(2004)
对所有非负整数都有f(x)=f(x-1)+f(x+1)且f(0)=2004`求f(2004)

对所有非负整数都有f(x)=f(x-1)+f(x+1)且f(0)=2004`求f(2004)
f(x+1) = f(x) - f(x-1)
f(x+2) = f(x+1) - f(x) = f(x) - f(x-1) - f(x) = -f(x-1)
可替换为
f(x) = - f(x-3) = f(x-6)
f(2004) = f(1998) = f(1992) = ……
2004/6 = 334
因此 f(2004) = f(0) = 2004