显示找到的17个结果中的1-10个。
莱布尼茨和谐三角形的第一个分子,然后分母(从左到右)。
+10 18
1, 1, 1, 2, 1, 2, 1, 3, 5, 6, 1, 3, 1, 4, 7, 12, 7, 12, 1, 4, 1, 5, 9, 20, 31, 30, 9, 20, 1, 5, 1, 6, 11, 30, 49, 60, 49, 60, 11, 30, 1, 6, 1, 7, 13, 42, 71, 105, 209, 140, 71, 105, 13, 42, 1, 7, 1, 8, 15, 56, 97, 168, 351, 280, 351, 280, 97, 168
评论
在这个三角形中,右边缘由正整数的倒数组成。不在这条边上的数字是通过将其上方对角的数字与紧邻其右侧的数字相加得到的。注意,在莱布尼茨的调和三角形中,我们将这两个数字相减,得到一个不在右手边的数字。
例子
1/1;
1/2, 1/2;
1/3, 5/6, 1/3;
1/4, 7/12, 7/12, 1/4;
1/5, 9/20, 31/30, 9/20, 1/5;
莱布尼茨和谐三角形的第一个分母,然后是分子(从左到右)。
+10 18
1, 1, 2, 1, 2, 1, 3, 1, 6, 5, 3, 1, 4, 1, 12, 7, 12, 7, 4, 1, 5, 1, 20, 9, 30, 31, 20, 9, 5, 1, 6, 1, 30, 11, 60, 49, 60, 49, 30, 11, 6, 1, 7, 1, 42, 13, 105, 71, 140, 209, 105, 71, 42, 13, 7, 1, 8, 1, 56, 15, 168, 97, 280, 351, 280, 351, 168, 97
例子
1/1; --> 1 1
1/2, 1/2; --> 2 1 2 1
1/3, 5/6, 1/3; --> 3 1 6 5 3 1
1/4, 7/12, 7/12, 1/4; --> 4 1 12 7 12 7 4 1
1/5, 9/20, 31/30, 9/20, 1/5; --> 5 1 20 9 30 31 20 9 5 1
在莱布尼茨的调和三角形中,先写分子,然后写每个元素的分母。
+10 16
1, 1, 1, 2, 1, 2, 1, 3, 1, 6, 1, 3, 1, 4, 1, 12, 1, 12, 1, 4, 1, 5, 1, 20, 1, 30, 1, 20, 1, 5, 1, 6, 1, 30, 1, 60, 1, 60, 1, 30, 1, 6, 1, 7, 1, 42, 1, 105, 1, 140, 1, 105, 1, 42, 1, 7, 1, 8, 1, 56, 1, 168, 1, 280, 1, 280, 1, 168, 1, 56, 1, 8, 1, 9, 1, 72, 1, 252, 1, 504, 1, 630, 1, 504, 1
参考文献
L.Comtet,《高级组合数学》,Reidel,1974年,第83页,问题25。
例子
1/1;
1/2, 1/2;
1/3, 1/6, 1/3;
1/4, 1/12, 1/12, 1/4;
1/5, 1/20, 1/30, 1/20, 1/5; ...
扩展
Gregory D Johnson提供的更多术语(gjohn(AT)iname.com)
1, 1, 1, 1, 5, 1, 1, 7, 7, 1, 1, 9, 31, 9, 1, 1, 11, 49, 49, 11, 1, 1, 13, 71, 209, 71, 13, 1, 1, 15, 97, 351, 351, 97, 15, 1, 1, 17, 127, 545, 1471, 545, 127, 17, 1, 1, 19, 161, 799, 2561, 2561, 799, 161, 19, 1, 1, 21, 199, 1121, 4159, 10625, 4159, 1121, 199, 21, 1
例子
1/1; --> 1
1/2, 1/2; --> 1 1
1/3, 5/6, 1/3; --> 1 5 1
1/4, 7/12, 7/12, 1/4; --> ...
1/5, 9/20, 31/30, 9/20, 1/5;
5, 7, 7, 9, 31, 9, 11, 49, 49, 11, 13, 71, 209, 71, 13, 15, 97, 351, 351, 97, 15, 17, 127, 545, 1471, 545, 127, 17, 19, 161, 799, 2561, 2561, 799, 161, 19, 21, 199, 1121, 4159, 10625, 4159, 1121, 199, 21
例子
1/1; -->
1/2, 1/2; -->
1/3, 5/6, 1/3; --> 5
1/4, 7/12, 7/12, 1/4; --> 7 7
1/5, 9/20, 31/30, 9/20, 1/5; --> 9 31 9
在莱布尼茨的类调和三角形中,先写元素的分子,然后写元素的分母(从左到右)的非平凡元素。也就是说A137752号.
+10 13
2, 2, 3, 5, 6, 3, 4, 7, 12, 7, 12, 4, 5, 9, 20, 31, 30, 9, 20, 5, 6, 11, 30, 49, 60, 49, 60, 11, 30, 6, 7, 13, 42, 71, 105, 209, 140, 71, 105, 13, 42, 7, 8, 15, 56, 97, 168, 351, 280, 351, 280, 97, 168, 15, 56, 8, 9, 17, 72, 127, 252, 545, 504, 1471
例子
1/1; -->
1/2, 1/2; --> 2 2
1/3, 5/6, 1/3; --> 3 5 6 3
1/4, 7/12, 7/12, 1/4; --> ...
1/5, 9/20, 31/30, 9/20, 1/5;
非平凡元素,首先写一个元素的分母,然后写莱布尼茨调和三角形中该元素的分子(从左到右)。也就是说A137753号.
+10 12
2, 2, 3, 6, 5, 3, 4, 12, 7, 12, 7, 4, 5, 20, 9, 30, 31, 20, 9, 5, 6, 30, 11, 60, 49, 60, 49, 30, 11, 6, 7, 42, 13, 105, 71, 140, 209, 105, 71, 42, 13, 7, 8, 56, 15, 168, 97, 280, 351, 280, 351, 168, 97, 56, 15, 8, 9, 72, 17, 252, 127, 504, 545, 630, 1471
例子
1/1; -->
1/2, 1/2; --> 2 2
1/3, 5/6, 1/3; --> 3 6 5 3
1/4, 7/12, 7/12, 1/4; --> ...
1/5, 9/20, 31/30, 9/20, 1/5;
奇数元素是指先写一个元素的分母,然后写莱布尼茨调和三角形中该元素的分子(从左到右)。也就是说A137753号.
+10 11
1, 1, 1, 1, 3, 1, 5, 3, 1, 1, 7, 7, 1, 5, 1, 9, 31, 9, 5, 1, 1, 11, 49, 49, 11, 1, 7, 1, 13, 105, 71, 209, 105, 71, 13, 7, 1, 1, 15, 97, 351, 351, 97, 15, 1, 9, 1, 17, 127, 545, 1471, 545, 127, 17, 9, 1, 1, 19, 161, 799, 2561, 2561, 799, 161, 19, 1
例子
1/1; --> 1 1
1/2, 1/2; --> 1 1
1/3, 5/6, 1/3; --> 3 1 5 3 1
1/4, 7/12, 7/12, 1/4; --> ...
1/5, 9/20, 31/30, 9/20, 1/5;
写莱布尼茨和谐三角形的奇数时,先写分子,然后写分母(从左到右)。
+10 10
1, 1, 1, 1, 1, 3, 5, 1, 3, 1, 7, 7, 1, 1, 5, 9, 31, 9, 1, 5, 1, 11, 49, 49, 11, 1, 1, 7, 13, 71, 105, 209, 71, 105, 13, 1, 7, 1, 15, 97, 351, 351, 97, 15, 1, 1, 9, 17, 127, 545, 1471, 545, 127, 17, 1, 9, 1, 19, 161, 799, 2561, 2561, 799, 161, 19, 1
例子
1/1; --> 1 1
1/2, 1/2; --> 1 1
1/3, 5/6, 1/3; --> 1 3 5 1 3
1/4, 7/12, 7/12, 1/4; -->
1/5, 9/20, 31/30, 9/20, 1/5;
交叉参考
囊性纤维变性。A003506号,A007622号,A046201美元,A046204号,A046205美元,A046206美元,A046208号,A046212号,A137752号,A137753号,A137754号,A137755号,A137756号,A137757号,A137758号.
在书写莱布尼茨和谐三角形的第一个分子和分母(从左到右)时,要写出不同的数字。
+10 9
1, 2, 3, 5, 6, 4, 7, 12, 9, 20, 31, 30, 11, 49, 60, 13, 42, 71, 105, 209, 140, 8, 15, 56, 97, 168, 351, 280, 17, 72, 127, 252, 545, 504, 1471, 630, 10, 19, 90, 161, 360, 799, 840, 2561, 1260, 21, 110, 199, 495, 1121, 1320, 4159, 2310, 10625, 2772
例子
1/1; --> 1
1/2, 1/2; --> 2
1/3, 5/6, 1/3; --> 3 5 6
1/4, 7/12, 7/12, 1/4; --> ...
1/5, 9/20, 31/30, 9/20, 1/5;
搜索在0.008秒内完成
|