Número icosaédrico

Dado un número n, encuentra el n-ésimo número icosaédrico. El número icosaédrico es una clase de número figurativo que representa un icosaedro (un poliedro con 20 caras.
Los primeros números icosaédricos son 1, 12, 48, 124, 255, 456, 742, 1128, 1629…………..

Ejemplos:  

Input : 5
Output :255

Input :10
Output :2260

El término n-ésimo del número icosaédrico viene dado por:

Implementación básica de la idea anterior:

// Icosahedral number to find
// n-th term in C++
#include <bits/stdc++.h>
using namespace std;
 
// Function to find
// Icosahedral number
int icosahedralnum(int n)
{
    // Formula to calculate nth
    // Icosahedral number &
    // return it into main function.
    return (n * (5 * n * n - 5 * n + 2)) / 2;
}
 
// Driver Code
int main()
{
    int n = 7;
 
    cout << icosahedralnum(n);
    return 0;
}

// Icosahedral number to find
// n-th term in C
#include <stdio.h>
 
// Function to find
// Icosahedral number
int icosahedralnum(int n)
{
    // Formula to calculate nth
    // Icosahedral number &
    // return it into main function.
    return (n * (5 * n * n - 5 * n + 2)) / 2;
}
 
// Driver Code
int main()
{
    int n = 7;
     
    printf("%d",icosahedralnum(n));
    return 0;
}
 
// This code is contributed by kothavvsaakash.

// Icosahedral number to find
// n-th term in Java
import java.io.*;
 
class GFG {
     
    // Function to find
    // Icosahedral number
    static int icosahedralnum(int n)
    {
        // Formula to calculate nth
        // Icosahedral number &
        // return it into main function.
         
        return (n * (5 * n * n - 5 *
                            n + 2)) / 2;
    }
 
    // Driver Code
    public static void main (String[] args)
    {
        int n = 7;
        System.out.println(
                        icosahedralnum(n));
    }
}
 
// This code is contributed by aj_36.

# Python 3 Program to find
# nth Icosahedral number
 
# Icosahedral number
# number function
def icosahedralnum(n) :
     
    # Formula to calculate nth
    # Icosahedral number
    # return it into main function.
    return (n * (5 * n * n -
                 5 * n + 2)) // 2
 
 
# Driver Code
if __name__ == '__main__' :
         
    n = 7
    print(icosahedralnum(n))
 
# This code is contributed aj_36

// Icosahedral number to
// find n-th term in C#
using System;
 
class GFG
{
     
    // Function to find
    // Icosahedral number
    static int icosahedralnum(int n)
    {
        // Formula to calculate
        // nth Icosahedral number
        // & return it into main
        // function.
        return (n * (5 * n * n -
                     5 * n + 2)) / 2;
    }
 
    // Driver Code
    static public void Main ()
    {
        int n = 7;
        Console.WriteLine(icosahedralnum(n));
    }
}
 
// This code is contributed by ajit

<?php
// Icosahedral number to
// find n-th term in PHP
 
// Function to find
// Icosahedral number
function icosahedralnum($n)
{
    // Formula to calculate nth
    // Icosahedral number &
    // return it into main function.
    return ($n * (5 * $n * $n -
                  5 * $n + 2)) / 2;
}
 
// Driver Code
$n = 7;
 
echo icosahedralnum($n);
 
// This code is contributed by m_kit
?>

<script>
    // Icosahedral number to
    // find n-th term in Javascript
     
    // Function to find
    // Icosahedral number
    function icosahedralnum(n)
    {
        // Formula to calculate
        // nth Icosahedral number
        // & return it into main
        // function.
        return (n * (5 * n * n - 5 * n + 2)) / 2;
    }
     
    let n = 7;
      document.write(icosahedralnum(n));
     
</script>

Producción: 

742

Tiempo Complejidad: O(1)
Espacio Auxiliar: O(1)