将正整数 n 拆分成 3 个不全相等的正整数相加，有几种不同的拆分法？

王守恩

Nicolas2050 发表于 2021-11-4 18:57
p(200) = 3972999029388

  我这里出不了200，100都出不了。  Table[Length@IntegerPartitions[n, n], {n, 0, 96}]
{1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 385, 490, 627, 792, 1002,
1255, 1575, 1958, 2436, 3010, 3718, 4565, 5604, 6842, 8349, 10143, 12310, 14883, 17977,
21637, 26015, 31185, 37338, 44583, 53174, 63261, 75175, 89134, 105558, 124754, 147273,
173525, 204226, 239943, 281589, 329931, 386155, 451276, 526823, 614154, 715220, 831820,
966467, 1121505, 1300156, 1505499, 1741630, 2012558, 2323520, 2679689, 3087735, 3554345,
4087968, 4697205, 5392783, 6185689, 7089500, 8118264, 9289091, 10619863, 12132164, 13848650,
15796476, 18004327, 20506255, 23338469, 26543660, 30167357, 34262962, 38887673, 44108109,
49995925, 56634173, 64112359, 72533807, 82010177, 92669720, 104651419, 118114304,

王守恩

Nicolas2050 发表于 2021-11-4 18:57
p(200) = 3972999029388

谢谢 Nicolas2050 ！   正整数 n 的拆分数 P(n)    A000041       
  
{1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 385, 490, 627, 792, 1002,
1255, 1575, 1958, 2436, 3010, 3718, 4565, 5604, 6842, 8349, 10143, 12310, 14883, 17977,
21637, 26015, 31185, 37338, 44583, 53174, 63261, 75175, 89134, 105558, 124754, 147273,

我就好奇 A000041 把好东西藏起来了。

1, 里面没有 10 楼的算法  P(200)=3972999029388

2, 没有 P(n)=Table\(\bigg[\)Length@IntegerPartitions\(\bigg[i, i\bigg], {i, 0, n}\bigg]\)

3, 也没有 P(n)=CoefficientList\(\bigg[\)Series\(\bigg[\)\(\displaystyle\prod_{i=1}^n\frac{1}{1-x^i},(x,0,n)\bigg],x\bigg]\)   

   这个是可以出来 200 的,  P(200)=3972999029388

王守恩

谢谢 Nicolas2050 ！   正整数 n 的拆分数 P(n)    A000041        
  
{1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 385, 490, 627, 792, 1002,
1255, 1575, 1958, 2436, 3010, 3718, 4565, 5604, 6842, 8349, 10143, 12310, 14883, 17977,
21637, 26015, 31185, 37338, 44583, 53174, 63261, 75175, 89134, 105558, 124754, 147273,

1. Table[PartitionsP[n], {n, 45}]

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