# 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;` `}` |

## 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

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