接 7 楼:把1个矩形(边长是整数)分成(分点在整数位置上)4个面积都是整数(>1)的三角形,
周边3个面积(不同)最大者不超过
4有01组: 2,4,3,
5有03组: 4,5,3, 2,5,4,
6有07组: 3,6,2, 5,6,2, 2,6,5, 3,4,6,
7有10组: 6,7,4, 4,7,5, 2,7,6,
8有16组: 6,8,2, 7,8,3, 6,8,5, 4,8,6, 2,8,7, 3,5,8,
9有23组: 4,9,2, 5,9,4, 8,9,5, 4,9,7, 2,9,8, 7,9,8, 5,8,9,
《数学研发论坛》网友 northwolves 给出前200项。谢谢 northwolves!
0,0,0, 1, 3, 7, 10, 16, 23, 36, 41, 60, 66, 85, 108, 132, 140, 176, 185, 227, 264, 298,
309, 372, 402, 442, 485, 553, 567, 662, 677, 743, 805, 859, 927, 1050, 1068, 1128,
1202, 1331, 1351, 1494, 1515, 1625, 1760, 1835, 1858, 2034, 2097, 2230, 2330, 2466,
2492, 2669, 2786, 2982, 3096, 3191, 3220, 3512, 3542, 3643, 3834, 4008, 4151, 4393,
4426, 4604, 4742, 5014, 5049, 5392, 5428, 5549, 5784, 5988, 6158, 6448, 6487, 6827,
7024, 7160, 7201, 7630, 7822, 7964, 8139, 8458, 8502, 8975, 9188, 9435, 9624, 9780,
9989, 10450, 10498, 10777, 11101, 11514, 11564, 11949, 12000, 12380, 12860, 13037,
13090, 13626, 13680, 14129, 14354, 14857, 14913, 15345, 15606, 15920, 16309, 16506,
16776, 17577, 17751, 17954, 18204, 18540, 18800, 19501, 19564, 19989, 20253, 20790,
20855, 21568, 21880, 22103, 22692, 23209, 23277, 23804, 23873, 24680, 24970, 25208,
25545, 26419, 26754, 26998, 27496, 27901, 27975, 28812, 28887, 29457, 29973, 30635,
30989, 31853, 31931, 32195, 32520, 33370, 33749, 34481, 34562, 35009, 35792, 36071,
36154, 37312, 37556, 38275, 38861, 39334, 39420, 40089, 40734, 41565, 41930, 42229,
42318, 43690, 43780, 44570, 44946, 45646, 46072, 46793, 47244, 47758, 48618, 49427,
49522, 50634, 50730, 51055, 51989, 52848, 52946, 54095, 54194, 55312, ..........
这可是一串在《整数序列在线百科全书(OEIS)》找不到的。
northwolves 特别指出:a(18)=176,a(19)=185;7楼的a(18)=166,a(19)=175是错误的。
且给出了a(18)=176的176个具体解。谢谢 northwolves! |