试了好多个终于搞定了
①[1,n](n >= 1) 1
②[2,1] 1
 [2,2] 2
 [2,n](n >= 2) 2
③[3,1] 1
 [3,2] 
 {
     [3,1] {(1,2)};
 } 2
 [3,3]
 {
   [3,2] {(1,1,1)}
 } 3
 [3,n](n >= 3) 3
 ···
 我一直试到第7个···，发现
 [i,j] = [i][j - 1] + [i - j][j]( j > 2 && j < i - 2);
 j == 1,[i][j] = 1;
 j == 2,[i][j] = i / 2 + 1;
 j > i - 1 && j <= i,[i][j] = [i][j - 1] + 1;
 j > i,[i][j] = [i][j - 1];
 ```
 ```
 #include<iostream>
#include<cstdio>
#include<cmath>
#include<cstring>
#include<algorithm>
#define LL long long
#define x first
#define y second
using namespace std;
const int N = 100;
int f[N][N];
void init()
{
    memset(f,0,sizeof(f));
    f[1][1] = 1;f[2][1] = 1;f[2][2] = 2;
    for(int i = 1;i <= 10;i ++)
      for(int j = 1;j <= 10;j ++)
      {
        if(j == 1)
        f[i][j ] = 1;
        else if(j == 2)
        f[i][j] = i / 2 + 1;
        else if(j < i - 1)
        f[i][j] = f[i][j - 1] + f[i - j][j];
        else if(j <= i)
        f[i][j] = f[i][j - 1] + 1;
        else
        f[i][j] = f[i][j - 1];
      }
      /*for(int i = 1;i <= 10;i ++)
      {
        for(int j = 1;j <= 10;j ++)
        cout<<f[i][j]<<" ";
        cout<<endl;
      }*/
}
int main()
{
    int t;
    scanf("%d",&t);
    init();
    while(t --)
    {
        int m,n;
        scanf("%d%d",&m,&n);
        cout<<f[m][n]<<endl;
    }
    return 0;
}

暴力搜索
#include<bits/stdc++.h>
#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstring>
#include<algorithm>
#include<queue>
#include<vector>
#include<stack>
#include<malloc.h>
#include<climits>
#include<map>
#define LL long long
#define x first
#define y second
using namespace std;
const int N = 500;
int num[N];
bool st[N],flag[20][N];
int n,m;
int ans;
bool check()//判断当前类别是否枚举过
{
    for(int i = 1;i <= m;i ++)
    if(!flag[i][num[i]])
    return true;
    return false;
}
void dfs(int u,int v,int k)
{
    if(v == m)
    { 
        ans ++;//计数
        //cout<<ans<<endl;
        for(int i = 1;i < m;i ++)//标记当前种类
        /*cout<<num[i]<<" ",*/flag[i][num[i]] = true;
        num[m] = k/*,cout<<k<<endl*/;
        flag[m][k] = true;
        return;
    }
    for(int i = u;i <= (k - i)/(m - v);i ++)
    {  

          num[v] = i; 
          if(num[v] >= num[v - 1])//按照递增顺序避免重复
          dfs(u,v + 1,k - i);//第v + 1位为u时
          if(!check())//看是否枚举过
          continue;
          if(num[v] >= num[v - 1])//按照递增顺序
          dfs(u + 1,v,k);//第v位为u + 1时
    }
}
int main()
{
    int t;
    scanf("%d",&t);
    while(t --)
    {
     scanf("%d%d",&n,&m);
    memset(flag,false,sizeof(flag));
    ans = 0;
    dfs(0,1,n); 
    cout<<ans<<endl;   
    }

    return 0;
}