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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

import math

def main():
    N = int(input())
    ans = [0]*(N+1)

    end = N

    for i in range(3,end+1):
        sn = i
        x = 1
        y = 1
        z = sn - 2
        try:
            ans[cal(x,y,z)] += func(i,x,y,z)
        except IndexError:
            pass
        while z >= math.ceil(sn / 2):
            y += 1
            z -= 1
            if x > z or y > z:
                break
            try:
                ans[cal(x,y,z)] += func(i,x,y,z)
            except IndexError:
                pass
            for j in range(y):
                x += 1
                z -= 1
                if x > z or y > z:
                    break
                try:
                    ans[cal(x,y,z)] += func(i,x,y,z)
                except IndexError:
                    pass
    
    for i in range(1,N+1):
        print(ans[i])
        

def func(n,x,y,z):
    if x == y and y == z and z == x:
        return 1
    elif x != y and y != z and z != x:
        return 6
    else:
        return 3

def cal(x,y,z):
    return x**2+y**2+z**2+x*y+y*z+z*x

main()