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):
def fx(n):
  s = [0]*(n+1)
  for i in range(1,10000):
    if (i+1+1)**2 - i*1 - 1*1 - 1*i > n: break
    for j in range(1, 10000):
      if (1+j+1)**2 - 1*j - j*1 - 1*1 > n : break
      for k in range(1, 10000):
        if (1+1+k)**2 - 1*1 - 1*k - k*1 > n: break
        formula = (i+j+k)**2 - i*j - j*k - k*i
        if formula <= n and formula > 0:
          s[formula] += 1
        if formula >= n:
          break
  return s


n = int(input())
s = fx(n)
for i in range(1,n+1):
  print(s[i])

Solution (Python):
n=int(input())
import math
for i in range(1,n+1):
    t=0
    for x in range(1,101):
        if (x**2)*6>i:
            break
        for y in range(x,101):
            if x**2+3*(y**2)+2*x*y>i:
                break
            B=(x+y)
            C=x**2+y**2+x*y-i
            r=(B**2-4*C)**0.5
            z1=(-B+r)/2
            z2=(-B-r)/2
            if z1.is_integer() and z1>0:
                if x==y and y==z1:
                    t+=1
                elif x!=y and y!=z1 and z1!=x:
                    t+=6
                else:
                    t+=3
            if z2.is_integer() and z2>0:
                if x==y and y==z2:
                    t+=1
                elif x!=y and y!=z2 and z2!=x:
                    t+=6
                else:
                    t+=3
    print(t)

Solution (Python):
n = int(input())

cnt = [0] * n
for x in range(1, int(n ** 0.5) + 1):
    for y in range(1, int(n ** 0.5) + 1):
        for z in range(1, int(n ** 0.5) + 1):
            num = (x + y) ** 2 - x * y + z * (x + y + z)
            if num <= n:
                cnt[num - 1] += 1
print(*cnt, sep="\n")

Solution (Python):
n = int(input())
f = {}
for x in range(1, n + 1):
    for y in range(1, int(max((n - x**2), 0)**0.5) + 2):
        for z in range(1, int(max((n - x**2 - y**2), 0)**0.5) + 2):
            a = x**2 + y**2 + z**2 + x * y + y * z + z * x
            try:
                f[a] += 1
            except BaseException:
                f[a] = 1
for i in range(1, n + 1):
    try:
        print(f[i])
    except BaseException:
        print(0)

Solution (Python):

well_known_i = ['', 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n = int(input())

for i in range(1,n+1) :
    print(well_known_i[i])

Solution (Python):
N = int(input())

N2 = int(N**0.5)

cnt = [0] * (90000)

for x in range(1,N2+1):
  for y in range(1,N2+1):
    for z in range(1,N2+1):
      xyz = x*x + y*y + z*z + x*y + y*z + z*x
      cnt[xyz] += 1

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

Solution (Python):
import math
import sys
sys.setrecursionlimit(10**9)

def mi(): return map(int,input().split())
def ii(): return int(input())
def isp(): return input().split()
def deb(text): print("-------\n{}\n-------".format(text))

INF=10**20
def main():
    N=ii()
    j = math.ceil((N+1)**0.5)

    ans = [0] * (N+1)
    for x in range(1,j+1):
        for y in range(1,j+1):
            for z in range(1,j+1):
                n = x**2+y**2+z**2+x*y+y*z+z*x
                if 1<=n<=N:
                    ans[n] += 1
            
        
    print(*ans[1:],sep="\n")

                


if __name__ == "__main__":
    main()

Solution (Python):
import sys

sys.setrecursionlimit(10 ** 7)
input = sys.stdin.readline
f_inf = float('inf')
mod = 10 ** 9 + 7


def resolve():
    n = int(input())

    res = [0] * (n + 10)
    for x in range(1, int(pow(n, 0.5)) + 1):
        for y in range(1, int(pow(n, 0.5)) + 1):
            for z in range(1, int(pow(n, 0.5)) + 1):
                t = pow(x, 2) + pow(y, 2) + pow(z, 2) + x * y + y * z + z * x
                if t <= n:
                    res[t] += 1

    for x in range(1, n + 1):
        print(res[x])


if __name__ == '__main__':
    resolve()