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 (
	"bufio"
	"fmt"
	"log"
	"math"
	"os"
	"strconv"
)

func main() {
	scanner := Scanner()
	n := ReadInt(scanner)

	// ans := make(map[int]int, n)
	// ans := make([]int, n+1)
	count := 0
	y := 0
	z := 0
	for i := 1; i <= n; i++ {
	B:
		for x := 1; x <= int(math.Sqrt(float64(i))); x++ {
			if int(math.Pow(float64(x), float64(2))+math.Pow(float64(y), float64(2))+math.Pow(float64(z), float64(2))+float64(x*y)+float64(y*z)+float64(z*x)) > i {
				break
			}
			for y := x; y <= int(math.Sqrt(float64(i))); y++ {
				if int(math.Pow(float64(x), float64(2))+math.Pow(float64(y), float64(2))+math.Pow(float64(z), float64(2))+float64(x*y)+float64(y*z)+float64(z*x)) > i {
					break
				}
				for z := y; z <= int(math.Sqrt(float64(i))); z++ {
					// fmt.Println(x, y, z, i)
					if int(math.Pow(float64(x), float64(2))+math.Pow(float64(y), float64(2))+math.Pow(float64(z), float64(2))+float64(x*y)+float64(y*z)+float64(z*x)) > i {
						break
					}
					if int(math.Pow(float64(x), float64(2))+math.Pow(float64(y), float64(2))+math.Pow(float64(z), float64(2))+float64(x*y)+float64(y*z)+float64(z*x)) == i {
						// fmt.Println(x, y, z, i, int(math.Pow(float64(x), float64(2))+math.Pow(float64(y), float64(2))+math.Pow(float64(z), float64(2))+float64(x*y)+float64(y*z)+float64(z*x)))
						if x == y && y == z {
							count++
							break B
						} else {
							count++
							count++
							count++
							break B
						}
					}
				}
			}
		}
		// ans[i] = count
		fmt.Println(count)
		count = 0
	}
	// for _, v := range ans {
	// 	fmt.Printf("%v\n", v)
	// }
}

func Scanner() *bufio.Scanner {
	scanner := bufio.NewScanner(os.Stdin)
	scanner.Split(bufio.ScanWords)
	return scanner
}

func ReadInt(scanner *bufio.Scanner) int {
	var t string

	if scanner.Scan() {
		t = scanner.Text()
	}

	n, err := strconv.Atoi(t)
	if err != nil {
		log.Fatal(err)
	}

	return n

}