# 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  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;  }

## 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

 

Output :

63
1159


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