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 Kotlin (1.3.71) (judge verdict: Accepted)

@file:Suppress("NOTHING_TO_INLINE", "EXPERIMENTAL_FEATURE_WARNING", "OVERRIDE_BY_INLINE")
//@file:OptIn(ExperimentalStdlibApi::class)

import java.io.PrintWriter
import kotlin.math.*
import kotlin.random.Random
import kotlin.collections.sort as _sort
import kotlin.collections.sortDescending as _sortDescending
import kotlin.io.println as iprintln


/** @author Spheniscine */
fun main() { _writer.solve(); _writer.flush() }

fun PrintWriter.solve() {
    //val startTime = System.nanoTime()

    val numCases = 1//readInt()
    case@ for(case in 1..numCases) {
        val n = readInt()

        val s = n.sqrtCeil()
        val F = IntArray(n+1)

        for(x in 1..s) for(y in 1..s) for(z in 1..s) {
            val r = x*x + y*y + z*z + x*y + y*z + z*x
            if(r <= n) F[r]++
        }

        for(i in 1..n) println(F[i])
    }

//    iprintln("Time: ${(System.nanoTime() - startTime) / 1000000} ms")
}

fun Int.sqrtCeil() = ceil(sqrt(toDouble())).toInt()

/** IO */
//@JvmField val INPUT = File("input.txt").inputStream()
//@JvmField val OUTPUT = File("output.txt").outputStream()
@JvmField val INPUT = System.`in`
@JvmField val OUTPUT = System.out

const val _BUFFER_SIZE = 1 shl 16
@JvmField val _buffer = ByteArray(_BUFFER_SIZE)
@JvmField var _bufferPt = 0
@JvmField var _bytesRead = 0

tailrec fun readChar(): Char {
    if(_bufferPt == _bytesRead) {
        _bufferPt = 0
        _bytesRead = INPUT.read(_buffer, 0, _BUFFER_SIZE)
    }
    return if(_bytesRead < 0) Char.MIN_VALUE
    else {
        val c = _buffer[_bufferPt++].toChar()
        if (c == '\r') readChar()
        else c
    }
}

fun readLine(): String? {
    var c = readChar()
    return if(c == Char.MIN_VALUE) null
    else buildString {
        while(c != '\n' && c != Char.MIN_VALUE) {
            append(c)
            c = readChar()
        }
    }
}
fun readLn() = readLine()!!

fun read() = buildString {
    var c = readChar()
    while(c <= ' ') {
        if(c == Char.MIN_VALUE) return@buildString
        c = readChar()
    }
    do {
        append(c)
        c = readChar()
    } while(c > ' ')
}
fun readInt() = read().toInt()
fun readDouble() = read().toDouble()
fun readLong() = read().toLong()
fun readStrings(n: Int) = List(n) { read() }
fun readLines(n: Int) = List(n) { readLn() }
fun readInts(n: Int) = List(n) { read().toInt() }
fun readIntArray(n: Int) = IntArray(n) { read().toInt() }
fun readDoubles(n: Int) = List(n) { read().toDouble() }
fun readDoubleArray(n: Int) = DoubleArray(n) { read().toDouble() }
fun readLongs(n: Int) = List(n) { read().toLong() }
fun readLongArray(n: Int) = LongArray(n) { read().toLong() }

@JvmField val _writer = PrintWriter(OUTPUT, false)

/** shuffles and sort overrides to avoid quicksort attacks */
private inline fun <T> _shuffle(rnd: Random, get: (Int) -> T, set: (Int, T) -> Unit, size: Int) {
    // Fisher-Yates shuffle algorithm
    for (i in size - 1 downTo 1) {
        val j = rnd.nextInt(i + 1)
        val temp = get(i)
        set(i, get(j))
        set(j, temp)
    }
}

@JvmField var _random: Random? = null
val random get() = _random ?: Random(0x594E215C123 * System.nanoTime()).also { _random = it }

fun IntArray.shuffle(rnd: Random = random) = _shuffle(rnd, ::get, ::set, size)
fun IntArray.sort() { shuffle(); _sort() }
fun IntArray.sortDescending() { shuffle(); _sortDescending() }

fun LongArray.shuffle(rnd: Random = random) = _shuffle(rnd, ::get, ::set, size)
fun LongArray.sort() { shuffle(); _sort() }
fun LongArray.sortDescending() { shuffle(); _sortDescending() }

fun DoubleArray.shuffle(rnd: Random = random) = _shuffle(rnd, ::get, ::set, size)
fun DoubleArray.sort() { shuffle(); _sort() }
fun DoubleArray.sortDescending() { shuffle(); _sortDescending() }

fun CharArray.shuffle(rnd: Random = random) = _shuffle(rnd, ::get, ::set, size)
inline fun CharArray.sort() { _sort() }
inline fun CharArray.sortDescending() { _sortDescending() }

inline fun <T: Comparable<T>> Array<out T>.sort() = _sort()
inline fun <T: Comparable<T>> Array<out T>.sortDescending() = _sortDescending()
inline fun <T: Comparable<T>> MutableList<out T>.sort() = _sort()
inline fun <T: Comparable<T>> MutableList<out T>.sortDescending() = _sortDescending()

fun `please stop removing these imports IntelliJ`() { iprintln(max(1, 2)) }

/** additional commons */
inline fun <T> Iterable<T>.sumByLong(func: (T) -> Long) = fold(0L) { acc, t -> acc + func(t) }
inline fun <T> Sequence<T>.sumByLong(func: (T) -> Long) = fold(0L) { acc, t -> acc + func(t) }
inline fun <T> Array<T>.sumByLong(func: (T) -> Long) = fold(0L) { acc, t -> acc + func(t) }
fun IntArray.sumLong() = fold(0L, Long::plus)