# Centered Octagonal Number

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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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

 ` `

Output

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

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