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):
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6,66,0,12,36,78,36,42,0,36,0,78,24,48,24,18,30,90,15,96,18,27,21,54,0,24,21,48,27,84,18,48,42,36,6,66,12,108,12,42,0,48,9,27,60,21,36,84,6,36,18,42,18,54,18,60,0,60,15,72,9,99,42,12,12,60,0,57,42,18,18,78,0,42,6,36,36,63,9,42,15,30,18,78,6,24,48,42,0,102,12,75,45,42,30,84,24,66,9,24,30,90,24,42,0,24,3,84,21,84,33,66,24,36,6,36,48,51,18,72,0,66,18,54,30,24,18,48,18,30,0,102,12,45,36,24,0,102,3,42,15,42,54,54,21,66,24,66,30,102,3,66,0,48,12,24,30,45,36,54,6,78,9,48,24,39,36,96,0,66,6,27,27,60,30,18,30,48,12,90,24,60,36,6,0,42,12,78,36,36,24,114,6,60,0,18,6,69,18,84,0,36,6,48,6,39,24,42,24,54,6,72,48,36,42,60,0,48,0,36,18,138,24,30,30,42,18,75,18,48,18,24,0,78,0,78,57,60,9,48,9,36,30,30,42,42,39,84,0,24,12,87,27,30,42,24,24,90,0,36,24,60,36,84,0,42,0,30,21,87,12,72,24,42,12,60,30,72,21,60,0,96,12,30,42,39,18,66,12,84,12,63,42,42,24,42,0,18,6,78,15,75,45,54,12,54,6,84,30,30,18,54,0,42,24,39,27,96,18,42,21,48,0,54,18,33,36,66,0,84,0,75,48,30,42,54,12,54,15,42,30,96,18,42,0,18,6,123,15,48,24,48,39,42,6,21,54,45,12,60,0,90,12,30,36,45,18,72,21,78,12,30,12,60,30,18,0,78,6,60,36,33,18,60,12,30,0,60,18,90,30,54,0,36,1,78,27,84,30,18,15,102,9,27,30,24,57,90,0,42,9,48,42,42,12,72,27,48,9,108,18,48,48,18,0,84,6,66,24,48,21,114,6,78,24,30,30,42,18,60,0,18,12,63,9,51,66,48,15,54,0,66,60,36,18,48,0,66,6,36,30,96,9,36,30,30,24,93,24,72,24,66,0,60,24,48,30,24,30,72,6,60,12,30,12,93,18,72,0,30,0,81,30,36,48,36,30,90,6,54,24,57,24,36,0,54,18,36,24,78,18,72,33,12,0,51,30,48,24,42,0,90,3,78,30,30,27,138,6,30,18,36,24,75,24,12,0,54,12,42,18,84,36,30,18,66,6,45,36,36,48,114,0,24,6,30,21,108,15,48,18,36,18,57,24,63,42,54,0,78,6,81,36,18,24,42,18,120,0,24,24,66,12,54,0,48,12,66,18,42,36,48,18,72,6,48,48,33,6,102,0,54,24,39,54,60,12,90,18,36,3,111,24,51,48,42,0,90,0,45,36,54,48,54,24,18,18,51,18,72,0,54,0,18,12,54,36,57,18,42,18,120,0,63,42,27,36,48,0,54,6,39,30,81,18,72,33,54,9,72,12,54,54,24,0,54,15,75,24,60,12,78,6,30,12,39,54,72,6,54,0,72,6,78,12,54,39,30,15,48,6,57,48,18,24,90,0,90,18,42,24,39,42,24,30,42,0,84,6,66,30,30,0,30,0,27,42,39,33,90,24,84,18,51,36,69,24,54,0,42,18,87,33,51,18,42,9,126,9,84,36,66,18,54,0,36,0,66,12,48,15,54,30,18,18,60,18,96,54,42,0,102,0,27,36,30,36,108,15,54,0,24,36,60,24,66,0,30,0,54,15,75,48,36,18,48,24,36,36,54,15,108,0,84,18]
N=int(input())
for i in range(N):
  print(f[i])

Solution (Python):
import math
n = int(input())
mylist = [int(math.sqrt(i)) for i in range(1,n+1)]
mylist = [0]+mylist

def main():
    for N in range(1,n+1):
        result = 0
        for x in range(1,mylist[N//3]+1):
            tempx = x**2
            for y in range(x, mylist[(N-x**2)//2]+1):
                tempy = y**2
                tempxy = x*y
                tempxandy = (x+y)/2
                tempnum = N-tempx-tempy-tempxy+tempxandy**2
                if tempnum <= 0:
                    break
                else:
                    if math.sqrt(tempnum)*2 == int(math.sqrt(tempnum)*2):
                        z = math.sqrt(tempnum)-tempxandy
                        
                        if z < y:
                            break
                        elif x != y and y != z:
                            result += 6
                        elif x == y and y == z:
                            result += 1
                        else:
                            result += 3
        print(result)
main()

Solution (Python):
r=range(1,99)
a=[0]*5**7
for x in r:
 for y in r:
  for z in r:a[x*(x+y+z)+y*(y+z)+z*z-1]+=1
print(*a[:int(input())])

Solution (Python):
from collections import Counter

N = int(input())

C = Counter(
    x * x + y * y + z * z + x * y + y * z + z * x
    for x in range(1, 105) for y in range(1, 105) for z in range(1, 105)
)

for i in range(1, N + 1):
    print(C[i])

Solution (Python):
import math
N = int(input())
ans = [0 for _ in range(10050)]
r_n = math.floor(math.sqrt(N))
count = 0
for x in range(1,r_n):
    for y in range(1,r_n):
        for z in range(1,r_n):
            n = x*x + y*y + z*z + x*y + y*z + z*x
            if n < 10050:
                ans[n]+=1
for i in range(N):
    print(ans[i+1])

Solution (Python):
import math
n = int(input())
ans = [0 for _ in range(10001)]

for x in range(1,100):
    for y in range(1,100):
        for z in range(1,100):
            t = x**2 + y**2 + z**2 + x*y + y*z + z*x 
            if t <= 10000:
                ans[t] += 1
for i in range(1,n+1):
    print(ans[i])

Solution (Python):
L = []
for A in range(2,2 * 10**2):
    for B in range(2,2 * 10 ** 2):
        for C in range(2,2 * 10 ** 2):
            tmp = A * A + B * B + C * C
            if tmp > 2 * 10 ** 4: break
            x = (A + B + C) //2 - A  
            y = (A + B + C) //2 - B
            z = (A + B + C) //2 - C  
            if x >= 1 and y>=1 and z >= 1 and \
                (x+y)**2+(y+z)**2+(z+x)**2 == tmp:
                L.append(tmp//2)
L.sort()
def counter(array):
    from collections import Counter
    return Counter(array)
c = counter(L)
N = int(input())
for i in range(1,N+1):
    print(c[i])

Solution (Python):
import sys


def input():
    return sys.stdin.readline().rstrip()


def main():
    N = int(input())
    dp = [0] * (N + 1)
    rt = int(N ** 0.5) + 1
    for i in range(1, rt):
        ii = i ** 2
        for j in range(1, i + 1):
            iji = ii + j ** 2 + i * j
            if iji + 1 + i + j > N:
                break
            for k in range(1, j + 1):
                c = iji + k ** 2 + i * k + j * k
                if c <= N:
                    l = 6
                    if i == j or j == k:
                        l = 3
                        if i == k:
                            l = 1
                    dp[c] += l
                else:
                    break
    print(*dp[1:N + 1], sep="\n")


if __name__ == "__main__":
    main()