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):


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)