Problem:
Score : 300 points

Problem Statement

Let f(n) be the number of triples of integers (x,y,z) that satisfy both of the following conditions:

1 \leq x,y,z

x^2 + y^2 + z^2 + xy + yz + zx = n

Given an integer N, find each of f(1),f(2),f(3),\ldots,f(N).

Constraints

All values in input are integers.

1 \leq N \leq 10^4

Input

Input is given from Standard Input in the following format:

N

Output

Print N lines. The i-th line should contain the value f(i).

Sample Input 1

20

Sample Output 1

0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
3
3
0
0

For n=6, only (1,1,1) satisfies both of the conditions. Thus, f(6) = 1.

For n=11, three triples, (1,1,2), (1,2,1), and (2,1,1), satisfy both of the conditions. Thus, f(6) = 3.

For n=17, three triples, (1,2,2), (2,1,2), and (2,2,1), satisfy both of the conditions. Thus, f(17) = 3.

For n=18, three triples, (1,1,3), (1,3,1), and (3,1,1), satisfy both of the conditions. Thus, f(18) = 3.

Solution in C (GCC 9.2.1) (judge verdict: Accepted)

#include <stdio.h>

int tri(int X,int Y,int Z){
    int s,s2=X+Y+Z,x,y,z;
    if(s2%2)return 0;
    s=s2/2;
    x=s-Y;
    y=s-Z;
    z=s-X;
    if(x<1||y<1||z<1) return 0;
    if(x!=y){
        if(y==z||z==x){
            return 3;
        }else{
            return 6;
        }
    }else{
        if(y==z){
            return 1;
        }else{
            return 3;
        }
    }
}

int f(int n){
    int X=2,XX=4,Y,YY,Z,ZZ,count=0,n2=2*n;
    while(XX+8<=n2){
        Y=2;
        YY=4;
        while(Y<=X && XX+YY+4<=n2){
            Z=2;
            ZZ=4;
            if((X+Y)%2){
                Z=3;
                ZZ=9;
            }
            while(Z<=Y && XX+YY+ZZ<=n2){
                if(XX+YY+ZZ==n2){
                    count +=tri(X,Y,Z);
                    break;
                }
                ZZ+=4*Z+4;
                Z+=2;
            }
            YY+=2*Y+1;
            Y+=1;
        }
        XX+=2*X+1;
        X+=1;
    }
    return count;
}

int main(){
    int i,n;
    scanf("%d",&n);
    for(i=1;i<=n;i++){
        printf("%d\n",f(i));
    }
    return 0;
}