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.



Sample input:
20


Sample output:
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
3
3
0
0

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline

'''

'''

from math import floor

res = [0] * (10**4+1)

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

def solve(n):
    global res

    count = 0
    limit = floor(n**0.5)+1

    for x in range(1, limit):
        for y in range(x, limit):
            for z in range(y, limit):
                #print(x, y, z)
                r = a(x, y, z)
                if r > n:
                    break
                elif x == y == z:
                    res[r] += 1
                elif x != y and y != z and x != z:
                    res[r] += 6
                else:
                    res[r] += 3
    
n = int(input())
solve(n)
for i in range(1, n+1):
    print(res[i])

Submission status: Accepted

Solution code:
# -*- coding: utf-8 -*-

N, = map(int, input().split())

ans = [0] * N

max_y = 10000+1
max_z = 10000+1

for x in range(1, 10000+1):
    if x >= max_y:
        break
    for y in range(x, 10000+1):
        if y >= max_z:
            max_y = y
            break
        for z in range(y, 10000+1):
            thr = x**2 + y**2 + z**2 + x*y + y*z + z*x
            if thr > N:
                max_z = z
                break
            if x==y and y==z:
                ans[thr-1] += 1
            elif x==y or y==z:
                ans[thr-1] += 3
            else:
                ans[thr-1] += 6

for a in ans:
    print(a)