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.



Sample input:
20


Sample output:
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
3
3
0
0

Submission status: Runtime Error

Solution code:
def main():
	n = int(input())
	s = 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    return s[:n]
  
print(*main())

Submission status: Runtime Error

Solution code:
n = 10**4
ans = [0]*10**4
for x in range(1,101):
    for y in range(1,101):
        for z in range(1,101):
            a = (x+y+z)**2 -(x*y+y*z+z*x)
            if a <= N:
                ans[a-1] += 1
for i in range(int(input())):
    print(ans[i])

Submission status: Runtime Error

Solution code:
N=int(input())
ans = [0]*N
for i in range(1,100):
    for j in range(1,100):
        for k in range(1,100):
            ans[i**2+j**2+k**2+i*j+j*k+i*k] += 1
for i in range(N):
    print(ans[i])

Submission status: Runtime Error

Solution code:
n=int(input())
import numpy as np
import math
rn=(n-4+1/4)**0.5-1/2
rn=math.ceil(rn)

r=[0]*n

for xx in np.arange(1,rn+1):
  xx2=xx**2
  for yy in np.arange(1,xx+1):
    xx2yy2xxyy=xx2+yy**2+xx*yy
    xxpyy=xx+yy
    tempr=xx2yy2xxyy+1+xxpyy
    if tempr>n: 
      break
    for zz in np.arange(1,yy+1):
      tempr=xx2yy2xxyy+zz**2+xxpyy*zz
      if tempr>n: 
        break
      else:
        r[tempr-1]=len(set([xx,yy,zz]))

for ii in range(n):
  rr=0
  if r[ii]==3:
    rr=6            
  elif r[ii]==2:
    rr=3
  elif r[ii]==1:
    rr=1
  print(rr)

Submission status: Runtime Error

Solution code:
import itertools
import math
import collections
​
def main():
    n = int(input())
​
    s = int(math.sqrt(n))
    a = list(itertools.product(range(1,s),repeat=3))
​
    ans = []
    for i in range(len(a)):
        t = a[i][0] ** 2 + a[i][1] ** 2 + a[i][2] ** 2 + a[i][0] * a[i][1] + a[i][1] * a[i][2] + a[i][2] * a[i][0]
        ans.append(t)
        # print(ans)
​
    c = collections.Counter(ans)
    for i in range(1,n+1):
        print(c[i])
        
        
main()