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Icosahedral Number

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Given a number n, find the n-th icosahedral number. The Icosahedral Number is class of figurative number that represents an icosahedron(a polyhedron with 20 faces.
The first few Icosahedral Numbers are 1, 12, 48, 124, 255, 456, 742, 1128, 1629…………..


Examples:  

Input : 5
Output :255

Input :10
Output :2260

n-th term of Icosahedral Number is given by:

I_{n}=\frac{n(5n^2-5n+2)}{2}


Basic implementation of the above idea:

C++

// 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;
}

                    

C

// 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.

                    

Java

// 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.

                    

Python3

# 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

                    

C#

// 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

<?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
?>

                    

Javascript

<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>

                    

Output: 

742


Time Complexity: O(1)
Auxiliary Space: O(1)



Last Updated : 19 May, 2022
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