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 JavaScript (Node.js 12.16.1) (judge verdict: Wrong Answer)

//let input = "20";

function main(input){
  input = input.trim();
  let n = parseInt(input);
  let count = 0;
  for(let i = 1; i<=n; i++){
    count = 0;
    let kaisuu = Math.floor(Math.sqrt(i)/2);
    for(let x = 1; x<=kaisuu+1; x++){
      for(let y = 1; y<=kaisuu+1; y++){
        for(let z = 1; z<=kaisuu+1; z++){
          if(x*x+y*y+z*z+x*y+y*z+z*x===i){
            count++;
          }
        }//z
      }//y
    }//x
    console.log(count);
  }//i
}
//main(input);
main(require("fs").readFileSync("/dev/stdin", "utf8"));