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Re:算不上是完整证明,大家可以补充一下

Posted by masque at 2009-10-15 20:04:18 on Problem 2680
In Reply To:算不上是完整证明,大家可以补充一下 Posted by:daryl at 2006-09-08 19:24:05
> 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
如此之精妙...我是发现了规律,证明不了...直接打表出来...

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