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Centered Octagonal Number
• Last Updated : 09 Apr, 2021

Given a number n, find the nth centered octagonal number.
A centered octagonal number represents an octagon with a dot in the centre and others dots surrounding the centre dot in the successive octagonal layer. Examples :

```Input :  2
Output : 9

Input : 5
Output : 81```

Centered Octagonal n-th Number is given by :

` `

Basic Implementation of the above approach:

## C++

 `// Program to find nth``// centered octagonal``// number``#include ``using` `namespace` `std;` `// Centered octagonal number function``int` `cen_octagonalnum(``long` `int` `n)``{``    ``// Formula to calculate nth``    ``// centered octagonal number &``    ``// return it into main function.``    ``return` `(4 * n * n - 4 * n + 1);``}` `// Driver Code``int` `main()``{``    ``long` `int` `n = 6;``    ``cout << n << ``"th  centered"``                 ``<< ``" octagonal number : "``;``    ``cout << cen_octagonalnum(n);``    ``cout << endl;``    ``n = 11;``    ``cout << n << ``"th  centered"``                  ``<< ``" octagonal number : "``;``    ``cout << cen_octagonalnum(n);` `    ``return` `0;``}`

## Java

 `// Java Program to find nth``// centered octagonal number``import` `java.io.*;`` ` `class` `GFG``{``     ` `    ``// Function to find centered``    ``// octagonal number``    ``static` `int` `centeredoctagonalNumber(``int` `n)``    ``{``        ``// Formula to calculate nth``        ``// centered octagonal number``        ``// and return it into main function``        ``return` `4` `* n * (n - ``1``) + ``1``;``    ``}``     ` `    ``// Driver Code``    ``public` `static` `void` `main(String args[])``    ``{``        ``int` `n = ``6``;``        ``System.out.print(n + ``"th centered "` `+``                       ``"octagonal number: "``);``        ``System.out.println(``                 ``centeredoctagonalNumber(n));``        ` `        ``n = ``11``;``        ``System.out.print(n + ``"th centered "` `+``                       ``"octagonal number: "``);``        ``System.out.println(``                  ``centeredoctagonalNumber(n));``         ` `    ``}``}` `// This code has been contributed by Prasad_Kshirsagar.`

## Python3

 `# Program to find nth``# centered octagonal number` `def` `cen_octagonalnum(n) :``    ` `    ``# Formula to calculate nth``    ``# centered octagonal number``    ``return` `(``4` `*` `n ``*` `n ``-``            ``4` `*` `n ``+` `1``)` `# Driver Code``if` `__name__ ``=``=` `'__main__'` `:``        ` `    ``n ``=` `6``    ``print``(n,``"th Centered"``,``            ``"octagonal number: "``,``             ``cen_octagonalnum(n))``    ``n ``=` `11``    ``print``(n,``"th Centered"` `,``            ``"octagonal number: "``,``             ``cen_octagonalnum(n))``                ` `# This code is contributed``# by akt_mit`

## C#

 `// Program to find nth centered octagonal``// number``using` `System;` `public` `class` `GFG{``    ` `    ``// Centered octagonal number function``    ``static` `long` `cen_octagonalnum(``long`  `n)``    ``{``        ` `        ``// Formula to calculate nth``        ``// centered octagonal number &``        ``// return it into main function.``        ``return` `(4 * n * n - 4 * n + 1);``    ``}``    ` `    ``// Driver code``    ``static` `public` `void` `Main ()``    ``{``        ``long` `n = 6;``        ``Console.WriteLine(n + ``"th centered"``                    ``+ ``" octagonal number : "``        ``+ cen_octagonalnum(n));``    ` `        ``n = 11;``        ``Console.WriteLine(n + ``"th centered"``                    ``+ ``" octagonal number : "``                    ``+ cen_octagonalnum(n));``    ``}``}` `// This code is contributed by anuj_67.`

## PHP

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## Javascript

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Output

```6th  centered octagonal number : 121
11th  centered octagonal number : 441```

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