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: Time Limit Exceeded)

process.stdin.resume();
process.stdin.setEncoding('utf8');

"use strict";
//x^2+y^2+z^2+xy+yz+zx=n
function calc(n) {
    let count=0
    for(let x=1; x<=n; x++) {
        for(let y=1; y<=n; y++) {
            const a = 1
            const b = x+y
            const c = x**2+y**2+x*y-n
            const judge = (b**2-4*a*c)
            if(judge>=0) {
                let z0 = (-b-judge**0.5)/(2*a)
                let z1 = (-b+judge**0.5)/(2*a)
                if((z0 >= 1 && z0===parseInt(z0,10)) || (z1 >= 1 && z1===parseInt(z1,10))) {
                    count++
                    const numUniq = [...new Set([x,y,Math.max(z0,z1)])].length
                    //console.log(numUniq)
                    if(numUniq === 2) count+=2
                    else if(numUniq === 3) count+=5
                    return count
                }
                /*
                if(z1 >= 1 && z1===parseInt(z1,10)) count++
                */
                //console.log(`x=${x}, y=${y}, z0=${z0},z1=${z1}`)
                
            }            
        }
    }
    return count
}

function main(arg) {
    const n = parseInt(arg)
    for(let i=1; i<=n; i++) {
        //console.log(`-------i=${i}-------`)
        let ans = calc(i)
        console.log(ans)
    }
}

main(require("fs").readFileSync("/dev/stdin", "utf8"));