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:
s = 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for i in range(int(input())):
    print(s[i])

Submission status: Accepted

Solution code:
import math


def main():
  N = int(input())

  dp = [0] * N

  lx = math.ceil(math.sqrt(N))

  for x in range(1, lx):
    x2 = x ** 2

    ly = math.ceil(math.sqrt(max(1, N - x2)))

    for y in range(1, ly):
      y2 = y ** 2
      lz = math.ceil(math.sqrt(max(1, N - x2 - y2 - (x * y))))

      for z in range(1, lz):
        z2 = z ** 2

        v = x2 + y2 + z2 + x * y + y * z + z * x
        if(v <= N):
          dp[v-1] += 1

  for v in dp:
    print(v)

if __name__ == "__main__":
  main()

Submission status: Accepted

Solution code:
n = int(input())

num = range(1, int(n ** 0.5) + 1)
from itertools import combinations_with_replacement
table = [0] * n
for i in combinations_with_replacement(num, 3):
    #print(i)
    index = (i[0] + i[1] + i[2]) ** 2 - (i[0] * i[1] + i[0] * i[2] + i[1] * i[2])

    if (i[0] + i[1] + i[2]) ** 2 - (i[0] * i[1] + i[0] * i[2] + i[1] * i[2]) > n:
        continue
    if i[0] == i[1] == i[2]:
        table[index - 1] += 1
    elif i[0] != i[1] != i[2]:
        table[index - 1] += 6
    else:
        table[index - 1] += 3
for i in range(n):
    print(table[i])

Submission status: Accepted

Solution code:
import math

n=int(input())
dp=[0]*(10**6)

for x in range(1,101):
    for y in range(1,101):
        for z in range(1,101):
            dp[x**2+y**2+z**2+x*y+y*z+z*x]+=1
for i in range(n):
    print(dp[i+1])

Submission status: Accepted

Solution code:
n = int(input())
t = [0]*10001
for i in range(1,41):
    t[6*i**2] += 1
for i in range(1,99):
    for j in range(1,99):
        if(i != j):
            a = (i+j)**2 + 2*j**2
            if(a <= 10000):
                t[a] += 3
            else:
                break
for i in range(3,100):
    for j in range(2,i):
        for k in range(1,j):
            a = ((i+j)**2 + (j+k)**2 + (k+i)**2)//2
            if(a <= 10000):
                t[a] += 6
            else:
                break
for i in range(1,n+1):
    print(t[i])

Submission status: Accepted

Solution code:
#n, m, q = map(int, input().split())
#List = list(map(int, input().split()))
#req = [list(map(int, input().split())) for _ in range(q)]
#t = t[:-1]
#print(ans[j], end = "") 改行無しで出力
#[0]*n
#sort = sorted(a)[::-1] 降順
n = int(input())
import itertools
List = [0]*100
List2 = [0]*60001

for i in range(100):
    List[i] = i+1

h = list(itertools.combinations_with_replacement(List, 3))

for j in range(len(h)):
    a = h[j][0]
    b = h[j][1]
    c = h[j][2]

    sum = a*a + b*b + c*c + a*b + b*c + c*a
    if a == b == c:
        List2[sum] += 1
    elif a == b or b == c or c == a:
        List2[sum] += 3
    else:
        List2[sum] += 6

for k in range(1, n+1):
    print(List2[k])

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
def main():
    N = int(input())
    max_x = 100
    max_y = 100
    max_z = 100
    ans = [0] * N
    for x in range(1, max_x+1):
        for y in range(1, max_y+1):
            for z in range(1, max_z+1):
                a = (x+y+z)**2 - x*y - y*z - z*x
                if 1 <= a <= N:
                    ans[a-1] += 1
    for ni in ans:
        print(ni)
if __name__ == "__main__":
    main()

Submission status: Accepted

Solution code:
import itertools
n=int(input())
mylist=[0]*n
a=1
while(6*(a**2)<n):
    a+=1
l=list(range(1,3*a-1))
for c in itertools.product(l,repeat=3):
    sum_num=sum(c)**2-(c[0]*c[1]+c[1]*c[2]+c[2]*c[0])
    if sum_num<=n:
        mylist[sum_num-1]+=1
for i in mylist:
    print(i)