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算不上是完整证明，大家可以补充一下In Reply To:找到了递推关系的规律,但找不到合理的解释,谁来解释一下? Posted by:yiyiyi4321 at 2005-11-05 10:29:52 0 1 1 01 2 10*01 3 01101001 4 10010110*01101001 5 01101001100101101001011001101001 <1>仔细看的话,就会发现 N为偶数时序列一定是1******1 N为偶数时序列一定是0******1 这个证明很简单 <2>N为偶数时 N所对应的序列就是N-1所对应序列关于左边的对称形式 而且当N为奇数时 最左边一定为零 所以可以得出 当N为偶数时 a[N]=a[N-1]*2+1 <3>N为奇数时 N所对应的序列左边一半是N-1所对应的序列 右边一半是N-2所对应序列关于右边的对称形式 结合<1>可以得出 a[N]=2*a[N-2]+a[N-1]=2*a[N-2]+1+a[N-1]-1=2*a[N-1]-1 Followed by:
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