https://www.reddit.com/r/algorithms/comments/57oiox/help_with_generating_algorithm/

cube.cpp

#include <bits/stdc++.h>

using namespace std;
typedef unsigned long long int ull;
typedef long long int ll;

#define debug(...) {fprintf(stderr, __VA_ARGS__);}

const int N = 5000;

ll memo[N][N];
int n, x;

int main () {
    scanf("%d %d", &n, &x);

    memo[n][0] = 1;
    for (int y = 1; y <= x; y++)
        memo[n][y] = 0;

    for (int i = n-1; i >= 0; i--) {
        memo[i][0] = 1;
        for (int y = 1; y <= x; y++) {
            memo[i][y] = memo[i+1][y-1];

            for (int j = i+2; j <= n; j++)
                memo[i][y] += memo[j][y];
        }
    }
    
    printf("%lld\n", memo[0][x]);
}

quadratic.cpp

#include <bits/stdc++.h>

using namespace std;
typedef unsigned long long int ull;
typedef long long int ll;

#define debug(...) {fprintf(stderr, __VA_ARGS__);}

const int N = 5000;

ll f[N][N];
ll f[N][N];
int n, x;

int main () {
    scanf("%d %d", &n, &x);

    f[n][0] = g[n][0] = 1;
    for (int y = 1; y <= x; y++) {
        f[n][y] = 0;
        g[n][y] = 0;
    }


    for (int i = n-1; i >= 0; i--) {
        g[i][0] = f[i][0] = 1;
        for (int y = 1; y <= x; y++) {
            f[i][y] = f[i+1][y-1] + g[i+1][y];
            g[i][y] = f[i+1][y] + g[i+1][y];
        }
    }
    printf("%lld\n", memo[0][x]);
}