número endecagonal

Dado un número n, la tarea es encontrar el n-ésimo número endecagonal. 
Un número endecagonal es un número figurado que extiende el concepto de números triangulares y cuadrados al decágono (polígono de once lados). El enésimo número endecágono cuenta el número de puntos en un patrón de n decágonos anidados, todos compartiendo una esquina común, donde el enésimo endecágono en el patrón tiene lados formados por i puntos separados una unidad entre sí.
Ejemplos: 
 

Entrada: 2 
Salida: 11
Entrada: 6 
Salida: 141 
 

Fórmula para el enésimo número endecagonal: 
 

// C++ program to find nth
// Hendecagonal number
#include <bits/stdc++.h>
using namespace std;
 
// Function to find
// Hendecagonal number
int hendecagonal_num(int n)
{
    // Formula to calculate nth
    // Hendecagonal number
    return (9 * n * n - 7 * n) / 2;
}
 
// Driver Code
int main()
{
    int n = 3;
    cout << n << "rd Hendecagonal number: ";
    cout << hendecagonal_num(n);
    cout << endl;
    n = 10;
    cout << n << "th Hendecagonal number: ";
    cout << hendecagonal_num(n);
 
    return 0;
}

// C program to find nth
// Hendecagonal number
#include <stdio.h>
 
// Function to find
// Hendecagonal number
int hendecagonal_num(int n)
{
    // Formula to calculate nth
    // Hendecagonal number
    return (9 * n * n - 7 * n) / 2;
}
 
// Driver Code
int main()
{
    int n = 3;
    printf("%drd Hendecagonal number: ",n);
    printf("%d\n",hendecagonal_num(n));
 
    n = 10;
    printf("%dth Hendecagonal number: ",n);
    printf("%d\n",hendecagonal_num(n));
 
    return 0;
}
 
// This code is contributed by kothavvsaakash.

// Java program to find nth
// Hendecagonal number
import java.io.*;
 
class GFG
{
     
// Function to find
// Hendecagonal number
static int hendecagonal_num(int n)
{
    // Formula to calculate nth
    // Hendecagonal number
    return (9 * n * n -
            7 * n) / 2;
}
 
// Driver Code
public static void main (String[] args)
{
int n = 3;
System.out.print(n + "rd Hendecagonal " +
                             "number: ");
System.out.println(hendecagonal_num(n));
 
n = 10;
System.out.print(n + "th Hendecagonal " +
                             "number: ");
System.out.println(hendecagonal_num(n));
}
}
 
// This code is contributed by ajit

# Program to find nth
# Hendecagonal number
 
# Function of Hendecagonal
# number
def hendecagonal_num(n) :
     
    # Formula to calculate nth
    # Hendecagonal number &
    # return it into main function.
     
    return (9 * n * n -
            7 * n) // 2
 
# Driver Code
if __name__ == '__main__' :
         
    n = 3
    print(n,"rd Hendecagonal number : " ,
                    hendecagonal_num(n))
 
    n = 10
    print(n,"th Hendecagonal number : " ,
                    hendecagonal_num(n))
 
# This code is contributed by ajit

// C# program to find nth
// Hendecagonal number
using System;
 
class GFG
{
// Function to find
// Hendecagonal number
static int hendecagonal_num(int n)
{
    // Formula to calculate nth
    // Hendecagonal number
    return (9 * n * n - 7 * n) / 2;
}
 
// Driver Code
static public void Main ()
{
    int n = 3;
    Console.Write(n +
                 "rd Hendecagonal number: ");
    Console.WriteLine( hendecagonal_num(n));
 
    n = 10;
    Console.Write(n +
                 "th Hendecagonal number: ");
    Console.WriteLine( hendecagonal_num(n));
    }
}
 
// This code is contributed by aj_36

<?php
// PHP program to find nth
// Hendecagonal number
 
// Function to find
// Hendecagonal number
 
function hendecagonal_num($n)
{
     
    // Formula to calculate nth
    // Hendecagonal number
    return (9 * $n * $n - 7 * $n) / 2;
}
 
// Driver Code
$n = 3;
echo $n , "th Hendecagonal number: ";
echo hendecagonal_num($n);
echo "\n";
     
$n = 10;
echo $n , "th Hendecagonal number: ";
echo hendecagonal_num($n);
 
// This code is contributed by m_kit
?>

<script>
    // Javascript program to find nth
    // Hendecagonal number
     
    // Function to find
    // Hendecagonal number
    function hendecagonal_num(n)
    {
        // Formula to calculate nth
        // Hendecagonal number
        return (9 * n * n - 7 * n) / 2;
    }
     
    let n = 3;
    document.write(n + "rd Hendecagonal number: ");
    document.write(hendecagonal_num(n) + "</br>");
    n = 10;
    document.write(n + "th Hendecagonal number: ");
    document.write(hendecagonal_num(n));
 
// This code is contributed by divyesh072019.
</script>

Producción : 
 

3th Hendecagonal number: 30
10th Hendecagonal number: 415

Complejidad de tiempo: O(1)
Espacio auxiliar: O(1)
Referencia: https://en.wikipedia.org/wiki/Polygonal_number