本帖最后由 王守恩 于 2021-11-6 09:52 编辑
谢谢白新岭！将正整数 n 拆分成 5 个不全相等的正整数相加，有a(n)种不同的拆分法。
例子
a(06)=01: (1,1,1,1,2)
a(07)=02: (1,1,1,1,3),(1,1,1,2,2)
a(08)=03: (1,1,1,1,4),(1,1,1,2,3),(1,1,2,2,2)
a(09)=05: (1,1,1,1,5),(1,1,1,2,4),(1,1,1,3,3),(1,1,2,2,3),(1,2,2,2,2)
a(10)=06: (1,1,1,1,6),(1,1,1,2,5),(1,1,1,3,4),(1,1,2,2,4),(1,1,2,3,3),(1,2,2,2,3)
a(11)=10: (1,1,1,1,7),(1,1,1,2,6),(1,1,1,3,5),(1,1,1,4,4),(1,1,2,2,5),(1,1,2,3,4),(1,1,3,3,3),(1,2,2,2,4),(1,2,2,3,3),(2,2,2,2,3)
a(12)=13: (1,1,1,1,8),(1,1,1,2,7),(1,1,1,3,6),(1,1,1,4,5),(1,1,2,2,6),(1,1,2,3,5),(1,1,2,4,4),(1,1,3,3,4),(1,2,2,2,5),(1,2,2,3,4),(1,2,3,3,3),(2,2,2,2,4),(2,2,2,3,3)
{1, 2, 3, 5, 6, 10, 13, 18, 23, 29, 37, 47, 57, 70, 83, 101, 119, 141, 164, 191, 221, 255, 291, 333, 376, 427, 480, 540, 603, 673, 748, 831, 918,
1014, 1114, 1226, 1342, 1469, 1602, 1746, 1898, 2062, 2233, 2418, 2610, 2818, 3034, 3266, 3507, 3764, 4033, 4319, 4616, 4932, 5259, 5608,
5969, 6351, 6747, 7165, 7599, 8056, 8529, 9027, 9541, 10083, 10642, 11229, 11835, 12469, 13125, 13811, 14518, 15257, 16018, 16814, 17633,
18487, 19366, 20281, 21224, 22204, 23212, 24260, 25336, 26455, 27604, 28796, 30020, 31288, 32591, 33940, 35324, 36756, 38224, 39744, 41301,
42910, 44559, 46261, 48006, 49806, 51649, 53550, 55495, 57501, 59553, 61667, 63829, 66054, 68331, 70673, 73067, 75529, 78044, 80631, 83273,
85987, 88759, 91605, 94512, 97495, 100540, 103664, 106851, 110121, 113456, 116875, 120362, 123934, 127578, 131310, 135114, 139009, 142978,
147042, 151182, 155418, 159733, 164146, 168642, 173238, 177918, 182702, 187571, 192548, 197613, 202787, 208052, 213428, 218899, 224484,
230165, 235963, 241859, 247877, 253995, 260236, 266581, 273051, 279629, 286335, 293150, 300097, 307155, 314349, 321657, 329103, 336666,
344369, 352194, 360162, 368253, 376491, 384854, 393369, 402012, 410808, 419736, 428820, 438040, 447419, 456936, 466616, 476436, 486424,
496555, 506856, 517304, 527924, 538696, 549644, 560745, 572026, 583463, 595085, 606866, 618834, 630965, 643286, 655775, 668457, 681309}
就这么简单的一串数，在《整数序列在线百科全书(OEIS)》好像找不到。
说明：5没有，4是有的。将正整数 n 拆分成 4 个不全相等的正整数相加，有a(n)种不同的拆分法。A331444(2020 年 1 月 22 日)
1, 2, 3, 4, 6, 9, 11, 14, 18, 23, 27, 33, 39, 47, 54, 63, 72, 84, 94, 107, 120, 136, 150, 168, 185, 206, 225, 248, 270, |
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