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Centered Octahedral number

• Last Updated : 19 Jul, 2021

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 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 Codeint main(){    int n = 3;    cout << centeredOctahedral(n) << endl;     n = 9;    cout << centeredOctahedral(n) << endl;     return 0;}

Java

 // Java Program to find nth// Centered octahedral numberimport 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 functiondef 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 Codeif __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 numberusing 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

 

Javascript

 
Output :

63
1159

Time Complexity: O(1)
Auxiliary Space: O(1)

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