Centered Octahedral number

Last Updated : 19 May, 2022

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:

\begin{math}Co_{n} = \frac{(2n+1)(2n^2+2n+3)}{3}

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 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# 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>