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:
n = int(input())

f = 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for i in range(n):
    print(f[i])

Submission status: Accepted

Solution code:
import sys, math, itertools, collections, bisect 
input = lambda: sys.stdin.buffer.readline().rstrip().decode('utf-8') 
inf = float('inf') ;mod = 10**9+7 
mans = inf ;ans = 0 ;count = 0 ;pro = 1

n = int(input())
for i in range(1, n+1):
    cnt = 0
    for x in range(1, int(math.sqrt(i+1))):
        for y in range(1, int(math.sqrt(i+1))):
            d = (x+y)**2 -4*(x*x + y*y + x*y - i)
            if d < 0:
                pass
            else:
                z = (-(x+y)+math.sqrt(d))/2
                if z == int(z) and z >= 1:
                    cnt += 1
    print(cnt)

Submission status: Accepted

Solution code:
"""
(x+y+z)^2 = (x^2+y^2+z^2) + 2(xy+yz+zx)
"""
def func(x, y, z): return (x + y + z) ** 2 - x * y - y * z - z * x


def main():
    num = int(input())
    counter = [0] * 20000
    # func(41, 41, 41) = 10086
    # func(99, 1, 1) = 10002
    for x in range(1, 100):
        for y in range(1, 100):
            for z in range(1, 123 - x - y + 1):
                tmp = func(x, y, z)
                counter[tmp] += 1
    for key, count in enumerate(counter):
        if key == 0:
            continue
        if key > num:
            break
        print(count)


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
# coding: utf-8
# Your code here!
N = int(input())

a = [0 for i in range(100**2 * 6 + 2)]

for x in range(1, 100):
    for y in range(1, 100):
        for z in range(1, 100):
            a[ x**2 + y**2 + z**2 + x*y + y*z + z*x ] += 1

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

Submission status: Accepted

Solution code:
#!/usr/bin/env pypy3

from math import sqrt
def count(k, t):
    if k*k - 4*t < 0: return 0
    if t == 0: return 0

    r = (-k + sqrt(k*k - 4*t)) / 2
    r = int(r)

    if r*r + k*r + t == 0 and 1 <= r: return 1
    return 0

def f(N):
    ret = 0
    for x in range(1, N+1):
        for y in range(1, N+1):
            k = x+y
            t = x*x + y*y + x*y - N
            # count solutions to z^2 + kz + t = 0
            ret += count(k, t)
    return ret


ans = dict()

for i in range(1, 10**4+1):
    ans[i] = 0

for x in range(1, 10**2+1):
    for y in range(1, 10**2+1):
        if (x**2 + y**2 > 10**4): continue
        for z in range(1, 10**2+1):
            n = x*x + y*y + z*z + x*y + x*z + y*z
            if n > 10**4: continue
            ans[n] += 1

N = int(input())
for i in range(1, N+1):
    print(ans[i])

Submission status: Accepted

Solution code:
def fx(x, y, z):
    return x**2 + y**2 + z**2 + x*y + y*z + z*x


n = int(input())

ind = {_: 0 for _ in range(1, 10**4 + 1)}
cnt = 0
for i in range(1, 10**4 + 1):
    if fx(i, 1, 1) > 10 ** 4:
        break
    for j in range(1, 10 ** 4 + 1):
        if fx(1, j, 1) > 10 ** 4:
            break
        for k in range(1, 10 ** 4 + 1):
            if fx(i, j, k) <= 10 ** 4:
                ind[fx(i, j, k)] += 1
            else:
                break

for num in range(1, n + 1):
    print(ind[num])

Submission status: Accepted

Solution code:
n = int(input())

a = [0] * 10010

# x,y,z
for x in range(1, 101):
  for y in range(1, 101):
    for z in range(1, 101):
      if x*x + y*y + z*z + x*y + y*z + z*x > n:
        continue
      a[x*x + y*y + z*z + x*y + y*z + z*x] += 1


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