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 in Go (1.14.1) (judge verdict: Time Limit Exceeded)

package main
 
import (
	"fmt"
)
 
var N, count int
var key string
var memo map[string]bool
func main() {
	fmt.Scan(&N)
	for i := 1; i <= N; i++ {
		count = 0
		memo = map[string]bool {}
		dp(1, 1, 1, i)
		fmt.Println(count)
	}
}

func dp (a, b, c, i int) {
	key = string(a) + string(b) + string(c)
	if memo[key] { return }
	ans := calc(a, b, c)
	if ans == i && !memo[key]{
	    memo[key] = true
		count++
		return
	}
	memo[key] = true
	if ans < i {
	  dp(a + 1, b, c, i)
	  dp(a , b + 1, c, i)
	  dp(a , b, c + 1, i)
	}
}

func calc(x, y, z int) int {
	return (x * x) + (y * y) + (z * z) + (x * y) + (y * z) + (z * x)
	//return x * (x + y + z) + y * (y + z) + z * z
}