Número Hexagonal Centrado

Dado un número n, encuentra el n-ésimo Número Hexagonal Centrado.
Un número hexadecagonal centrado representa un punto en el centro y otros puntos a su alrededor en sucesivas capas hexadecagonales (polígono de 16 lados).

Los primeros números hexadecagonales centrados son: 
1, 17, 49, 97, 161, 241, 337, 449, 577, 721, 881………………….

Ejemplos:

Input :  3
Output : 49

Input : 10
Output : 721

En matemáticas, el número hexagonal centrado para el término n-ésimo viene dado por:

A continuación se muestra la implementación básica de la idea anterior:

// C++ Program to find
// nth centered hexadecagonal
// number
#include <bits/stdc++.h>
using namespace std;
 
// centered hexadecagonal function
int center_hexadecagonal_num(long int n)
{
    // Formula to calculate nth
    // centered hexadecagonal number
    return 8 * n * n - 8 * n + 1;
}
 
// Driver Code
int main()
{
    long int n = 2;
    cout << n << "th centered hexadecagonal number : "
                    << center_hexadecagonal_num(n);
    cout << endl;
    n = 12;
    cout << n << "th centered hexadecagonal number : "
                    << center_hexadecagonal_num(n);
 
    return 0;
}

// C Program to find
// nth centered hexadecagonal
// number
#include <stdio.h>
 
// centered hexadecagonal function
int center_hexadecagonal_num(long int n)
{
    // Formula to calculate nth
    // centered hexadecagonal number
    return 8 * n * n - 8 * n + 1;
}
 
// Driver Code
int main()
{
    long int n = 2;
    printf("%ldth centered hexadecagonal number : %d\n",n,center_hexadecagonal_num(n));
 
    n = 12;
    printf("%ldth centered hexadecagonal number : %d\n",n,center_hexadecagonal_num(n));
 
    return 0;
}
 
// This code is contributed by kothavvsaakash.

// Java Program to find nth
// centered hexadecagonal number
import java.io.*;
 
class GFG
{
    // centered hexadecagonal function
    static int center_hexadecagonal_num(int n)
    {
        // Formula to calculate nth
        // centered hexadecagonal number
        return 8 * n * n -
               8 * n + 1;
    }
     
    // Driver Code
    public static void main(String args[])
    {
        int n = 2;
        System.out.print(n + "th centered " +
                    "hexadecagonal number: ");
        System.out.println(center_hexadecagonal_num(n));
         
        n = 12;
        System.out.print(n + "th centered " +
                    "hexadecagonal number: ");
        System.out.println(center_hexadecagonal_num(n));
    }
}
 
// This code is contributed by ajit.

# Program to find nth
# centered hexadecagonal
# number
 
# centered hexadecagonal
# function
def center_hexadecagonal_num(n):
     
    # Formula to calculate
    # nth centered hexadecagonal
    # number
    return 8 * n * n - 8 * n + 1
 
# Driver Code
if __name__ == '__main__' :
         
    n = 2
    print(n,"nd centered hexadecagonal " +
                              "number : ",
              center_hexadecagonal_num(n))
    n = 12
    print(n,"th centered hexadecagonal " +
                              "number : ",
              center_hexadecagonal_num(n))
                 
# This code is contributed
# by akt_mit

// C# Program to find nth
// centered hexadecagonal number
using System;
 
class GFG
{
     
    // centered hexadecagonal
    // function
    static int center_hexadecagonal_num(int n)
    {
        // Formula to calculate nth
        // centered hexadecagonal number
        return 8 * n * n -
               8 * n + 1;
    }
     
    // Driver Code
    static public void Main ()
    {
        int n = 2;
        Console.Write(n + "th centered " +
                    "hexadecagonal number: ");
        Console.WriteLine(center_hexadecagonal_num(n));
         
        n = 12;
        Console.Write(n + "th centered " +
                    "hexadecagonal number: ");
        Console.WriteLine(center_hexadecagonal_num(n));
    }
}
 
// This code is contributed by m_kit

<?php
// PHP Program to find
// nth centered hexadecagonal
// number
 
// centered hexadecagonal function
function center_hexadecagonal_num($n)
{
    // Formula to calculate nth
    // centered hexadecagonal number
    return 8 * $n * $n - 8 * $n + 1;
}
 
// Driver Code
$n = 2;
echo $n , "th centered hexadecagonal number : ",
                   center_hexadecagonal_num($n);
echo "\n";
$n = 12;
echo $n , "th centered hexadecagonal numbe : ",
                  center_hexadecagonal_num($n);
 
// This code is contributed by ajit
?>

<script>
 
// Javascript Program to find nth
// centered hexadecagonal number
 
// Centered hexadecagonal function
function center_hexadecagonal_num(n)
{
     
    // Formula to calculate nth
    // centered hexadecagonal number
    return 8 * n * n - 8 * n + 1;
}
 
// Driver code
var n = 2;
document.write(n + "th centered " +
               "hexadecagonal number: ");
document.write(center_hexadecagonal_num(n) + "<br>");
 
n = 12;
document.write(n + "th centered " +
               "hexadecagonal number: ");
document.write(center_hexadecagonal_num(n));
 
 
// This code is contributed by Ankita saini
 
</script>

Producción : 

2th centered hexadecagonal number : 17
12th centered hexadecagonal number : 1057

Complejidad temporal: O(1)
Espacio auxiliar: O(1)
Referencias: 
http://oeis.org/A069129