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來稿時間:2016年2月27日。
貼博時間:2016年3月2日。
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◆訊息◆2016年2月27日下午3:39分。
万先生:
您好!
前几天发现我的学生李绍详的拼合方法不能形成递推,属于特殊的拼合个例,于是从头开始,经过我们艰苦的努力终于找到了统一的参数,即可以根据统一的参数得到统一的制作公式。现在才算真正地彻底解决了2^N阶N-1次类自然数幻方。
其中黄剑潮和李绍祥都付出了艰辛的努力,彻底解决这个课题与他们的努力十分不开的。
四川達州:钟明
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◆回復◆2016年2月28日傍晚6:55分。
剛出外回港,收到如此好的結果,……不為自然數千百的幻方難過,只為類自然數(lzrs)今天的幻方歡呼,你們的辛勤的建築,今天是個人的,明天是數學世界的。
後人必會為我們今天共同開拓了類自然數(lzrs)幻方而感到驕傲!
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◆手機欣賞版◆
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◆電腦欣賞版◆
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2^N阶N-1次类自然数幻方的统一参数 |
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作者 钟明 黄剑潮 李绍祥 |
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8阶2次类自然数幻方参数 |
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A | B |
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C=MOD(A+B,2) |
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0 | 0 | 1 | 0 | 1 | 0 |
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0 | 1 | 1 |
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0 | 0 | 1 | 1 | 0 | 0 |
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1 | 0 | 1 |
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1 | 1 | 1 | 0 | 1 | 0 |
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1 | 0 | 1 |
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0 | 0 | 0 | 1 | 0 | 0 |
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1 | 0 | 0 |
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0 | 0 | 1 | 0 | 0 | 1 |
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0 | 0 | 0 |
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0 | 1 | 1 | 0 | 0 | 0 |
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0 | 1 | 1 |
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1 | 0 | 1 | 1 | 1 | 1 |
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0 | 1 | 0 |
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16阶3次类自然数幻方参数 |
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A | B |
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C=MOD(A+B,2) |
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0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 |
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0 | 1 | 1 | 0 |
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0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 |
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1 | 0 | 1 | 1 |
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1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 |
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1 | 0 | 1 | 1 |
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0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
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1 | 0 | 0 | 0 |
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0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 |
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0 | 0 | 0 | 0 |
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0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 |
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0 | 1 | 1 | 0 |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
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0 | 0 | 0 | 1 |
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0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
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0 | 0 | 0 | 1 |
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1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
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0 | 1 | 0 | 0 |
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32阶4次类自然数幻方参数 |
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A | B |
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C=MOD(A+B,2) |
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0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 |
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0 | 1 | 1 | 0 | 0 |
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0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 |
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1 | 0 | 1 | 1 | 0 |
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1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 |
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1 | 0 | 1 | 1 | 0 |
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0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
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1 | 0 | 0 | 0 | 0 |
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0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 |
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0 | 0 | 0 | 0 | 0 |
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0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 |
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0 | 1 | 1 | 0 | 0 |
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0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 |
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0 | 0 | 0 | 1 | 1 |
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0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 |
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0 | 0 | 0 | 1 | 1 |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
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0 | 0 | 0 | 0 | 1 |
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0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
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0 | 0 | 0 | 0 | 1 |
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1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
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0 | 1 | 0 | 0 | 0 |
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64阶5次类自然数幻方参数 |
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A | B |
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0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 |
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0 | 1 | 1 | 0 | 0 | 0 |
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0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
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1 | 0 | 1 | 1 | 0 | 0 |
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1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 |
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1 | 0 | 1 | 1 | 0 | 0 |
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0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
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1 | 0 | 0 | 0 | 0 | 0 |
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0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 |
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0 | 0 | 0 | 0 | 0 | 0 |
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0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
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0 | 1 | 1 | 0 | 0 | 0 |
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0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
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0 | 0 | 0 | 1 | 1 | 0 |
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0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
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0 | 0 | 0 | 1 | 1 | 0 |
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0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 |
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0 | 0 | 0 | 0 | 1 | 1 |
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0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
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0 | 0 | 0 | 0 | 1 | 1 |
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0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
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0 | 0 | 0 | 0 | 0 | 1 |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
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0 | 0 | 0 | 0 | 0 | 1 |
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1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
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0 | 1 | 0 | 0 | 0 | 0 |
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从8阶2次到2^N阶N-1次类自然数幻方的参数规律 |
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0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
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0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
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0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
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1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
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1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
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1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
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1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
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0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
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0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
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0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
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0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
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0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
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0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
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0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
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0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
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0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 |
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0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
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0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 |
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0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
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0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 |
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0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
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0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 |
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0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
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0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
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0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
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1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
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0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
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2^N阶N-1次类自然数幻方参数的统一模型 |
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0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ... | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ... |
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0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ... | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ... |
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1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ... | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ... |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ... | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ... |
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0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ... | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ... |
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0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ... | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ... |
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0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | ... | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ... |
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0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ... | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | ... |
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0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | ... | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | ... |
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0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | ... | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | ... |
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0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | ... | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | ... |
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0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | ... | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | ... |
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0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | ... | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | ... |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | ... | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | ... |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | ... | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | ... |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | ... | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | ... |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | ... | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | ... |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | ... | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | ... |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | ... | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | ... |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | ... | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | ... |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | ... | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ... |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ... | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | ... |
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... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
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1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ... | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ... |
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上次的結果;
http://m.blog.chinaunix.net/uid-20489909-id-5613949.html
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★特別指出,8階2次→16階3次→32階4次→64階5次→128階6次→256階7次→512階8次的全程詳細推演,由於片幅過大,博客吃不消,因此略過了。
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只貼了以上的;
◆8階2次~64階5次的過程。
◆8階2次到2^N階N-1次類自然數(lzrs)幻方的參數規律。
◆2^N階N-1次類自然數(lzrs)幻方參數的統一模型。
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有關8階~512階各種參數的更詳細操作,……有需要的朋友可聯繫我索取。
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