Octahedral Number

Given a number n, the task is to find n-th octahedral number.
A octahedral number belongs to a figurate number and it is the number of spheres in an octahedron built from closely packed spheres. First few octahedral numbers (where n = 0, 1, 2, 3…….) are : 0, 1, 6, 19 and so on.

Examples :

Input : 4
Output : 44



Input : 8
Output : 344

Formula for nth octahedral number:

n * (2n2+1) / 3

C++

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// C++ program to find nth
// octahedral number
#include <bits/stdc++.h>
using namespace std;
  
// Function to find
// octahedral number
int octahedral_num(int n)
{
    // Formula to calculate nth
    // octahedral number
    return n * (2 * n * n + 1) / 3;
}
  
// Drivers code
int main()
{
    int n = 5;
  
    // print result
    cout << n << "th Octahedral number: ";
    cout << octahedral_num(n);
    return 0;
}

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Java

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// Java program to find nth octahedral
// number
import java.io.*;
  
class GFG {
  
    // Function to find octahedral number
    static int octahedral_num(int n)
    {
  
        // Formula to calculate nth
        // octahedral number
        // and return it into main function.
        return n * (2 * n * n + 1) / 3;
    }
  
    // Driver Code
    public static void main(String[] args)
    {
        int n = 5;
        // print result
        System.out.print(n + "th Octahedral"
                         + " number: ");
        System.out.println(octahedral_num(n));
    }
}

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Python3

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# Python 3 program to find nth
# octahedral number
  
# Function to find
# octahedral number
def octahedral_num(n) :
      
    # Formula to calculate nth
    # octahedral number
    return n * (2 * n * n + 1) // 3
  
# Driver Code
if __name__ == '__main__' :
          
    n = 5
    print(n,"th Octahedral number: "
                , octahedral_num(n))
  
# This code is contributed ajit.

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C#

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// C# program to find nth 
// Octahedral number
using System;
  
class GFG
{
      
    // Function to find 
    // octahedral number
    static int octahedral_num(int n)
    {
  
        // Formula to calculate 
        // nth octahedral number
        // and return it into 
        // main function.
        return n * (2 * n * 
                    n + 1) / 3;
    }
  
    // Driver Code
    static public void Main ()
    {
        int n = 5;
          
        // print result
        Console.Write(n + "th Octahedral"
                        + " number: ");
        Console.WriteLine(octahedral_num(n));
    }
}
  
// This code is Contributed by m_kit

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PHP

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<?php
// PHP program to find nth
// octahedral number
   
   
// Function to find
// octahedral number
function octahedral_num( $n)
{
    // Formula to calculate nth
    // octahedral number
    // and return it into main function.
    return $n * (2 * $n * $n + 1) / 3;
}
   
// Drivers Code
$n = 5;
   
// print result
echo $n, "th Octahedral number: ";
echo octahedral_num($n);
   
?> 

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Output :

5th Octahedral number: 85

Reference: https://en.wikipedia.org/wiki/Octahedral_number



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