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Centered decagonal number
• Last Updated : 09 Apr, 2021

Given a number n, find the nth Centered decagonal number .
A Centered Decagonal Number is centered figurative number that represents a decagon with dot in center and all other dot surrounding it in successive decagonal form. Source[Wiki] The first few Centered Decagonal Numbers are :
1, 11, 31, 61, 101, 151, 211, 281, 361, 451, 551, 661…………
Examples :

```Input :  3
Output : 31

Input : 6
Output : 151```

In mathematics centered decagonal number for n-th term is given by :

` `

Below is the basic implementation of the above idea.

## C++

 `// Program to find nth``// centered decagonal``// number``#include ``using` `namespace` `std;` `// Centered decagonal``// number function` `int` `centereddecagonalnum(``int` `n)``{``    ``// Formula to calculate nth``    ``// centered decagonal number &``    ``// return it into main function.``    ``return` `(5 * n * n + 5 * n + 1);``}` `// Driver Code``int` `main()``{``    ``int` `n = 5;``    ``cout << n << ``"th centered decagonal"``                          ``<< ``"number: "``;``    ``cout << centereddecagonalnum(n);``    ``cout << endl;``    ``n = 9;``    ``cout << n << ``"th centered decagonal"``                          ``<< ``"number: "``;``    ``cout << centereddecagonalnum(n);` `    ``return` `0;``}`

## Java

 `// Java Program to find nth``// centered decagonal number``import` `java.io.*;` `class` `GFG``{``    ` `    ``// Centered decagonal``    ``// number function``    ``static` `int` `centereddecagonalnum(``int` `n)``    ``{``        ` `    ``// Formula to calculate nth``    ``// centered decagonal number &``    ``// return it into main function.``    ``return` `(``5` `* n * n + ``5` `* n + ``1``);``    ``}` `    ``// Driver Code``    ``public` `static` `void` `main (String[] args)``    ``{``        ``int` `n = ``5``;``        ``System.out.print(n + ``"th centered "` `+``                       ``"decagonal number: "``);``        ``System.out.println(centereddecagonalnum(n));` `        ``n = ``9``;``        ``System.out.print(n + ``"th centered "` `+``                       ``"decagonal number: "``);``        ``System.out.println(centereddecagonalnum(n));``    ``}``}` `// This code is contributed by m_kit`

## Python3

 `# Program to find nth``# centered decagonal number` `# Centered decagonal``# number function``def` `centereddecagonalnum(n) :``    ` `    ``# Formula to calculate``    ``# nth centered decagonal``    ``# number & return it``    ``# into main function.``    ``return` `(``5` `*` `n ``*` `n ``+``            ``5` `*` `n ``+` `1``)` `# Driver Code``if` `__name__ ``=``=` `'__main__'` `:``        ` `    ``n ``=` `5``    ``print``(n,``"th centered decagonal "` `+``                          ``"number : "``,``              ``centereddecagonalnum(n))` `    ``n ``=` `9``    ``print``(n,``"th centered decagonal "` `+``                          ``"number : "``,``              ``centereddecagonalnum(n))``              ` `# This code is contributed by m_kit`

## C#

 `// Program to find nth``// centered decagonal``// number``using` `System;` `class` `GFG``{``// Centered decagonal``// number function``static` `int` `centereddecagonalnum(``int` `n)``{``    ``// Formula to calculate nth``    ``// centered decagonal number &``    ``// return it into main function.``    ``return` `(5 * n * n + 5 * n + 1);``}` `// Driver Code``static` `public` `void` `Main ()``{``int` `n = 5;``Console.Write(n + ``"th centered decagonal"``+``                              ``"number: "``);``Console.WriteLine(centereddecagonalnum(n));` `n = 9;``Console.Write(n + ``"th centered decagonal"``+``                              ``"number: "``);``Console.WriteLine(centereddecagonalnum(n));``}``}` `// This code is contributed by aj_36`

## PHP

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## Javascript

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Output

```5th centered decagonalnumber: 151
9th centered decagonalnumber: 451```

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