Icosahedral Number

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) Source : Wiki).

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++

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// 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;
}

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Java

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// 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.

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Python3

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# 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

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C#

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// 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

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PHP

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<?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
?>

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Output

742


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Improved By : jit_t