连等式猜想

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上面的拼凑是杂乱的，想要证明它，还得找一些规律。以下是我的一种思路，到了后面则卡住了，故以“猜想”发此文.

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后面有试证，但无果！
郁闷中.......，改日再发.......

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Treenewbee

试着穷举了一下，以n=3为例，至少有23种表示方法：

{{1,2,5,3,7,9,4,6,8},{1,2,5,4,6,9,3,7,8},{1,2,6,3,9,8,4,5,7},{1,2,6,5,7,8,3,4,9},{1,2,8,7,9,6,3,4,5},{1,4,2,3,5,6,7,8,9},{2,4,5,1,9,8,3,6,7},{2,4,5,3,7,8,1,6,9},{2,4,6,3,9,7,1,5,8},{2,4,7,5,9,6,1,3,8},{2,4,8,7,9,5,1,3,6},{2,8,3,5,7,4,1,6,9},{2,8,4,7,9,3,1,5,6},{3,6,4,1,7,8,2,5,9},{3,6,5,1,9,7,2,4,8},{3,6,5,2,8,7,1,4,9},{3,6,8,7,9,4,1,2,5},{4,8,2,1,3,9,5,6,7},{4,8,5,1,9,6,2,3,7},{4,8,5,3,7,6,1,2,9},{4,8,6,3,9,5,1,2,7},{6,9,4,1,5,8,2,3,7},{6,9,8,5,7,4,1,2,3}}

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今天脑补了一下，觉得应该能证明了，待整理给出

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续4楼

王守恩

Treenewbee 发表于 2024-5-19 13:45
试着穷举了一下，以n=3为例，至少有23种表示方法：

{{1,2,5,3,7,9,4,6,8},{1,2,5,4,6,9,3,7,8},{1,2,6,3 ...

无端的觉得这串数应该有解？来几个试试？谢谢！
\(n=2,\frac{1}{2}=\frac{5}{10}=\frac{分子的和}{分母的和}\)
\(n=3,\frac{1}{4}=\frac{9}{36}\)
\(n=4,\frac{1}{6}=\frac{15}{90}\)
\(n=5,\frac{1}{9}=\frac{21}{189}\)
\(n=6,\frac{1}{13}=\frac{27}{351}\)
\(n=7,\frac{1}{17}=\frac{35}{595}\)
\(n=8,\frac{1}{21}=\frac{45}{945}\)
\(n=9,\frac{1}{26}=\frac{55}{1430}\)

A186351——2, 4, 6, 9, 13, 17, 21, 26, 32, 38, 44, 51, 59, 67, 75, 84, 94, 104, 114, 125, 137, 149,  

{5, 9, 15, 21, 27, 35, 45, 55, 65, 77, 91, 105, 119, 135, 153, 171, 189, 209, 231, 253, 275, 299, 325}

1. Table[((n + 1) (n + 2) - 1 + I^((n - 1) n))/2, {n, 2, 29}]

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{10, 36, 90, 189, 351, 595, 945, 1430, 2080, 2926, 4004, 5355, 7021, 9045, 11475, 14364, 17766}

1. Table[((n + 1) (n + 2) (n (n + 3) - 4) + 4 - 4 I^((n - 1) n))/8, {n, 2, 29}]

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