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• Last Updated : 13 Jul, 2021

Given a number n, find the nth Centered Octadecagonal number.
The Centered Octadecagonal Number represents a dot in the centre and others dot are arranged around it in successive layers of octadecagon(18 sided polygon). Examples :

```Input :  2
Output : 19

Input : 6
Output : 271```

In mathematics, Centered Octadecagonal number for n-th term is given by:

` `

Below is the basic implementation of the above idea:

## C++

 `// C++ Program to find the``// nth centered octadecagonal``// number``#include ``using` `namespace` `std;` `// centered octadecagon  function``int` `center_octadecagon_num(``long` `int` `n)``{``    ``// Formula to calculate nth``    ``// centered octadecagonal number``    ``return` `9 * n * n - 9 * n + 1;``}` `// Driver Code``int` `main()``{``    ``long` `int` `n = 3;``    ``cout << n << ``"th centered octadecagonal number : "``                  ``<< center_octadecagon_num(n);``    ``cout << endl;``    ``n = 13;``    ``cout << n << ``"th centered octadecagonal number : "``                 ``<< center_octadecagon_num(n);` `    ``return` `0;``}`

## Java

 `// Java Program to find the``// nth centered octadecagonal``// number``import` `java.io.*;` `class` `GFG``{``    ` `// centered octadecagon function``static` `int` `center_octadecagon_num(``int` `n)``{``        ` `    ``// Formula to calculate nth``    ``// centered octadecagonal number``    ``return` `9` `* n * n - ``9` `* n + ``1``;``}` `// Driver Code``public` `static` `void` `main (String[] args)``{``int` `n = ``3``;``System.out.print(n + ``"th centered "` `+``           ``"octadecagonal number : "``);``System.out.println(center_octadecagon_num(n));` `n = ``13``;``System.out.print(n + ``"th centered "` `+``           ``"octadecagonal number : "``);``System.out.println(center_octadecagon_num(n));``}``}` `// This code is contributed by ajit`

## Python3

 `# Program to find nth``# centered octadecagonal number` `# Centered octadecagonal``# number function``def` `center_octadecagon_num(n) :``    ` `    ``# Formula to calculate``    ``# nth centered octadecagonal``    ``# number & return it``    ``# into main function.``    ``return``(``9` `*` `n ``*` `n ``-``           ``9` `*` `n ``+` `1``)` `# Driver Code``if` `__name__ ``=``=` `'__main__'` `:``        ` `    ``n ``=` `3``    ``print``(n,``"rd centered octadecagonal "` `+``                                ``"number : "``,``                ``center_octadecagon_num(n))` `    ``n ``=` `13``    ``print``(n,``"th centered octadecagonal "` `+``                              ``"number : "``,``                ``center_octadecagon_num(n))``            ` `# This code is contributed``# by akt_mit`

## C#

 `// C# Program to find the``// nth centered octadecagonal``// number``using` `System;` `class` `GFG``{``    ` `// centered octadecagon function``static` `int` `center_octadecagon_num(``int` `n)``{``        ` `    ``// Formula to calculate nth``    ``// centered octadecagonal number``    ``return` `9 * n * n - 9 * n + 1;``}` `// Driver Code``static` `public` `void` `Main ()``{``    ` `    ``int` `n = 3;``    ``Console.Write( n + ``"th centered "` `+``            ``"octadecagonal number : "``);``    ``Console.WriteLine( center_octadecagon_num(n));` `    ``n = 13;``    ``Console.Write( n + ``"th centered "` `+``            ``"octadecagonal number : "``);``    ``Console.WriteLine(center_octadecagon_num(n));``}``}` `// This code is contributed by aj_36.`

## PHP

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## Javascript

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Output :

```3th centered octadecagonal number : 55
13th centered octadecagonal number : 1405```

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

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