Centered Octahedral number

We are given a number n, we need to find n-th centered octahedral number.
Description: A centered octahedral number is a figurate number. It counts the number of points of a three-dimensional integer lattice that lie inside an octahedron centered at the origin. The same numbers are special cases of the Delannoy numbers, which count certain two-dimensional lattice paths.
The First Few Centered octahedral numbers (where n = 0, 1, 2, 3…….) are : 
1, 7, 25, 63, 129, 231, 377, 575, 833, 1159…………………………. 
Mathematics formula for nth Centered octahedral number: 

Examples :

Input : n = 6
Output : 377

Input : n = 15
Output : 4991

C++

// C++ Program to find nth
// Centered octahedral number
#include <bits/stdc++.h>
using namespace std;

// Function to find
// Centered octahedral number

int centeredOctahedral(int n)
{
    // Formula to calculate nth
    // Centered octahedral number
    // and return it into main function.
    return (2 * n + 1) * (2 * n * n + 2 * n + 3) / 3;
}

// Driver Code
int main()
{
    int n = 3;
    cout << centeredOctahedral(n) << endl;

    n = 9;
    cout << centeredOctahedral(n) << endl;

    return 0;
}

C

// C Program to find nth
// Centered octahedral number
#include <stdio.h>

// Function to find
// Centered octahedral number
int centeredOctahedral(int n)
{
    // Formula to calculate nth
    // Centered octahedral number
    // and return it into main function.
    return (2 * n + 1) * (2 * n * n + 2 * n + 3) / 3;
}

// Driver Code
int main()
{
    int n = 3;
    printf("%d\n",centeredOctahedral(n));

    n = 9;
    printf("%d\n",centeredOctahedral(n));

    return 0;
}

// This code is contributed by kothavvsaakash.

Java

// Java Program to find nth
// Centered octahedral number
import java.io.*;

class GFG
{
    // Function to find
    // Centered octahedral number
    static int centeredOctahedral(int n)
    {

    // Formula to calculate nth
    // Centered octahedral number
    // and return it into main function.

    return (2 * n + 1) *
           (2 * n * n + 2 * n + 3) / 3;
    }

    // Driver Code
    public static void main (String[] args)
    {
    int n = 3;
    System.out.print( centeredOctahedral(n));
    System.out.println();
    n = 9;
    System.out.print(centeredOctahedral(n));
    }
}

// This code is contributed by aj_36

Python3

# Python 3 Program to find nth
# Centered octahedral number

# Centered octahedral
# number function
def centeredOctahedral(n) :

    # Formula to calculate nth
    # Centered octahedral number
    # return it into main function.
    return (2 * n + 1) * (
            2 * n * n +
            2 * n + 3) // 3

# Driver Code
if __name__ == '__main__' :

    n = 3
    print(centeredOctahedral(n))
    n = 9
    print(centeredOctahedral(n))

# This code is contributed ajit

C#

// C# Program to find nth
// Centered octahedral number
using System;

public class GFG {

    // Function to find
    // Centered octahedral number
    static int centeredOctahedral(int n)
    {

        // Formula to calculate nth
        // Centered octahedral number
        // and return it into main function.

        return (2 * n + 1) *
            (2 * n * n + 2 * n + 3) / 3;
    }

    // Driver Code
    static public void Main ()
    {
        int n = 3;
        Console.WriteLine(
               centeredOctahedral(n));

        n = 9;
        Console.WriteLine(
              centeredOctahedral(n));
    }
}

// This code is contributed by m_kit.

PHP

<?php
// PHP Program to find nth
// Centered octahedral number

// Function to find
// Centered octahedral number
function centeredOctahedral($n)
{
    // Formula to calculate
    // nth Centered octahedral
    // number and return it
    // into main function.
    return (2 * $n + 1) *
           (2 * $n * $n +
            2 * $n + 3) / 3;
}

// Driver Code
$n = 3;
echo centeredOctahedral($n), "\n";

$n = 9;
echo centeredOctahedral($n), "\n";

// This code is contributed ajit
?>

Javascript

<script>

// Javascript Program to find nth
// Centered octahedral number

// Function to find
// Centered octahedral number
function centeredOctahedral(n)
{

    // Formula to calculate nth
    // Centered octahedral number
    // and return it into main function.

    return (2 * n + 1) *
           (2 * n * n + 2 * n + 3) / 3;
}


// Driver Code

var n = 3;
document.write(centeredOctahedral(n));
document.write("<br>");

n = 9;
document.write(centeredOctahedral(n));

// This code is contributed by Kirti

</script>

Output :

63
1159

Time Complexity: O(1)
Auxiliary Space: O(1)
Reference: 
https://en.wikipedia.org/wiki/Centered_octahedral_number