Octahedral Number

Given a number n, the task is to find n-th octahedral number. 
An octahedral number belongs to a figurate number and it is the number of spheres in an octahedron built from closely packed spheres. First, a 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++

// 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;
}

Java

// 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));
    }
}

Python3

# 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.

C#

// 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

PHP

<?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);

?>

Javascript

<script>

// JavaScript 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
let n = 5;

// print result
document.write( n+ "th Octahedral number: ");
document.write(octahedral_num(n));

// This code is contributed by Bobby

</script>

Output

5th Octahedral number: 85

Time Complexity: O(1) because constant operations are being performed
Auxiliary Space: O(1)

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