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: Accepted

Solution code:
import sys

def left(x, y, z):
    return x**2 + y**2 + z**2 + x*y + y*z + z*x

def count(x, y, z):
    uniq_num = len(set([x, y, z]))
    if uniq_num == 3:
        return 6  # 3!
    elif uniq_num == 2:
        return 3  # 3C1
    else:
        return 1

def show_result(ans):
    for n,fn in enumerate(ans[1:]):
        print(fn)

N = int(input())

ans = [0]*(N+1)
x = y = z = 1
while x <= N-3 and left(x, y, z) <= N:
    while y <= N-3 and left(x, y, z) <= N:
        while z <= N-3 and left(x, y, z) <= N:
            l = left(x, y, z)
            ans[l] += count(x, y, z)
            z += 1
        y += 1
        z = y
    x += 1
    y = z = x
show_result(ans)

Submission status: Accepted

Solution code:
n = int(input())

isEnd = False
sum = [0]*n

for x in range(1,100):
    x2 = x*x
    for y in range(1,100):
        sum_xy = x2 + y*(x+y)
        if sum_xy > n:
            break
        for z in range(1,100):
            tmp = sum_xy + z*(x+y+z)
            if tmp > n:
                break
            if tmp <= n:
                sum[tmp-1]+=1
for s in sum:
    print (s)

Submission status: Accepted

Solution code:
import collections
N = int(input())
l = []
for x in range(1, 101):
    for y in range(1, 101):
        for z in range(1, 101):
            f = x**2 + y**2 + z**2 + x*y + y*z + z*x
            l.append(f)
answer = collections.Counter(l)
for i in range(1, N+1):
    print(answer[i])

Submission status: Accepted

Solution code:
n=int(input())
l = [[0] for _ in range(n)]
lim=int(n**0.5)
l2=list(range(1, lim+1)) 
import itertools
for x in range(1, lim):
  for y in range(1, lim):
    for z in range(1, lim):
      d=x**2+y**2+z**2+x*y+x*z+y*z
      #print(d)
      #print(v)
      if d<=n:
        l[d-1][0]+=1
for i in l:
  print(i[0])

Submission status: Accepted

Solution code:
n = int(input())

l = 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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]

for i in range(0, n):
    print(l[i])

Submission status: Accepted

Solution code:
import itertools

N = int(input())

A = list(itertools.combinations_with_replacement(range(1,100),3))

Ans = [0 for i in range(1, N+1)]

for i in range(len(A)):
    f = int(((A[i][0]+A[i][1])**2 + (A[i][1]+A[i][2])**2 + (A[i][2] + A[i][0])**2)/2)
    if f <= N:
        if len(set(A[i])) == 1:
            Ans[f - 1] += 1
        elif len(set(A[i])) == 2:
            Ans[f - 1] += 3
        else:
            Ans[f - 1] += 6

for i in range(N):
    print(Ans[i])

Submission status: Accepted

Solution code:
n = int(input())


ans = []

def anscnt(x,y,z):
  if (x == y) & (y == z):
    return 1
  if (x == y) or (y == z) or (z == x):
    return 3
  return 6
  
def getval(x,y,z):
  return (x + y + z) ** 2 - (x *y + y*z + z * x)
  
for k in range(1,n+1):
  anslist = []
  
  x,y,z = 1,1,1
  
  while True: #x
    while True: #y
      while True: #z
        val = getval(x,y,z)
        if val == k :
          anslist.append( anscnt(x,y,z) )
          break
        elif val > k:
          break
        z += 1
        
      y += 1
      z = y
      if getval(x,y,z) > k:
        break
    x += 1
    y = x
    z = x
    if getval(x,y,z) > k:
      break
  ans.append( sum(anslist) )
  #print(anslist)
_ = [print(i) for i in ans ]