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 (Python):


import sys, math
sys.setrecursionlimit(300000)


def solve(N: int):
    n = math.ceil(N ** 0.5)
    ret = [0] * (N + 1)
    for x in range(1, n + 1):
        for y in range(1, n + 1):
            for z in range(1, n + 1):
                s = x * x + y * y + z * z + x * y + y * z + z * x
                if 1 <= s <= N:
                    ret[s] += 1
    for i in range(N):
        print(ret[i + 1])
    return

def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  
    solve(N)

if __name__ == '__main__':
    main()

Solution (Python):
import itertools
import math
N=int(input())

a = [0] * N

b = [1,1,1]

if N >= 6:
    for x,y,z in itertools.combinations_with_replacement(list(range(1,int(math.sqrt(N)) +1 )), 3):
        f = x**2 +y**2 +z**2 + x*y + y*z + x*z
        if f <= N:
            if x==y==z:
                a[f-1] += 1
            elif x==y or y== z:
                a[f-1] += 3
            else:
                a[f-1] += 6
        
        
[print(ans) for ans in a]