Buggy python submission (verdict: Time Limit Exceeded):
def f(x, y, z):
    return (x+y+z)**2 - x*y - y*z - z*x

  
N = int(input())
pattern = []

for x in range(1, 101):
    for y in range(1, 101):
        for z in range(1, 101):
            pattern.append(f(x, y, z))

for i in range(1, N+1):
    print(pattern.count(i))


Fixed submission:
def f(x, y, z):
    return (x+y+z)**2 - x*y - y*z - z*x


N = int(input())
for i in range(1, N+1):
    ans = 0
    for x in range(1, int(i**0.5)+2):
        for y in range(x, int(i**0.5)+2):
            if f(x, y, y-1) >= i:
                break
            l = y - 1
            r = int(i**0.5) + 1
            while r >= l:
                z = (r+l) // 2
                if f(x, y, z) == i:
                    if x < y:
                        if x == z or y == z:
                            ans += 3
                        else:
                            ans += 6
                    else:
                        if z == y:
                            ans += 1
                        else:
                            ans += 3
                if f(x, y, z) > i:
                    r = z - 1
                else:
                    l = z + 1

    print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
def f(x, y, z):
    return (x+y+z)**2 - x*y - y*z - z*x


N = int(input())
for i in range(1, N+1):
    ans = 0
    for x in range(1, int(i**0.5)+2):
        for y in range(1, int(i**0.5)+2):
            if x**2 + y**2 + x*y >= i:
                break
            l = 0
            r = int(i**0.5) + 1
            while r >= l:
                z = (r+l) // 2
                if f(x, y, z) == i:
                    ans += 1
                if f(x, y, z) > i:
                    r = z - 1
                else:
                    l = z + 1

    print(ans)


Fixed submission:
def f(x, y, z):
    return (x+y+z)**2 - x*y - y*z - z*x


N = int(input())
for i in range(1, N+1):
    ans = 0
    for x in range(1, int(i**0.5)+2):
        for y in range(x, int(i**0.5)+2):
            if f(x, y, y-1) >= i:
                break
            l = y - 1
            r = int(i**0.5) + 1
            while r >= l:
                z = (r+l) // 2
                if f(x, y, z) == i:
                    if x < y:
                        if x == z or y == z:
                            ans += 3
                        else:
                            ans += 6
                    else:
                        if z == y:
                            ans += 1
                        else:
                            ans += 3
                if f(x, y, z) > i:
                    r = z - 1
                else:
                    l = z + 1

    print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
def f(x, y, z, n):
    if (x+y+z)**2 - x*y - y*z - z*x == n:
        return True
    return False


N = int(input())
for i in range(1, N+1):
    ans = 0
    for x in range(1, int(i**0.5)+2):
        for y in range(x, int(i**0.5)+2):
            for z in range(y, int(i**0.5)+2):
                if f(x, y, z, i):
                    if x == y == z:
                        ans += 1
                    elif x == y or y == z or z == x:
                        ans += 3
                    else:
                        ans += 6
    print(ans)


Fixed submission:
def f(x, y, z):
    return (x+y+z)**2 - x*y - y*z - z*x


N = int(input())
for i in range(1, N+1):
    ans = 0
    for x in range(1, int(i**0.5)+2):
        for y in range(x, int(i**0.5)+2):
            if f(x, y, y-1) >= i:
                break
            l = y - 1
            r = int(i**0.5) + 1
            while r >= l:
                z = (r+l) // 2
                if f(x, y, z) == i:
                    if x < y:
                        if x == z or y == z:
                            ans += 3
                        else:
                            ans += 6
                    else:
                        if z == y:
                            ans += 1
                        else:
                            ans += 3
                if f(x, y, z) > i:
                    r = z - 1
                else:
                    l = z + 1

    print(ans)