Centered dodecahedral number

Given a number n, find then-th Centered Dodecahedral Number.

A Centered Dodecahedral number is class of figurative number.It is formed by a central dot, surrounded by successive dodecahedral(polyhedral with 12 flat surfaces) layers.

The first few Centered dodecahedral numbers (where n = 0, 1, 2, 3…….) are :
1, 33, 155, 427, 909, 1661 ……………

Examples:

```Input : 5
Output : 1661

Input :1
Output :33
```

Mathematical formula for the nth Centered dodecahedral number is given by:

```
```

Below is the basic implementation of the above idea:

C++

 `// Program to find nth centered  ` `// dodecahedral number ` `#include ` `using` `namespace` `std; ` ` `  `// Function to find ` `// centered dodecahedral number ` `int` `CenteredDodecahedral_num(``long` `int` `n) ` `{ ` `    ``// Formula to calculate nth ` `    ``// centered dodecahedral number ` `    ``// and return it into main function. ` `    ``return` `(2 * n + 1) * (5 * n * n + 5 * n + 1); ` `} ` `// Driver Code ` `int` `main() ` `{ ` `    ``long` `int` `n = 3; ` `    ``// print result ` `    ``cout << n << ``"th Centered Dodecahedral number : "``; ` `    ``cout << CenteredDodecahedral_num(n) << endl; ` ` `  `    ``n = 10; ` `    ``// print result ` `    ``cout << n << ``"th Centered Dodecahedral number : "``; ` `    ``cout << CenteredDodecahedral_num(n); ` ` `  `    ``return` `0; ` `} `

Java

 `// Java Program to find nth ` `// centered dodecahedral number ` `import` `java.io.*; ` ` `  `class` `GFG { ` ` `  `    ``// Function to find centered ` `    ``// dodecahedral number ` `    ``static` `int` `CenteredDodecahedral_num(``int` `n) ` `    ``{ ` `         `  `        ``// Formula to calculate nth ` `        ``// centered dodecahedral number ` `        ``// and return it into main function. ` `         `  `        ``return` `(``2` `* n + ``1``) *  ` `                     ``(``5` `* n * n + ``5` `* n + ``1``); ` `    ``} ` `     `  `    ``// Driver Code ` `    ``public` `static` `void` `main (String[] args) ` `    ``{ ` ` `  `        ``int` `n = ``3``; ` `         `  `        ``// print result ` `        ``System.out.print( n + ``"th Centered "` `                ``+ ``"Dodecahedral number : "``); ` `        ``System.out.println ( ` `                ``CenteredDodecahedral_num(n)); ` ` `  `        ``n = ``10``; ` `         `  `        ``// print result ` `        ``System.out.print( n + ``"th Centered "` `                ``+ ``"Dodecahedral number : "``); ` `        ``System.out.println(  ` `               ``CenteredDodecahedral_num(n)); ` `    ``} ` `} ` ` `  `// This code is contributed by m_kit. `

Python3

 `# Program to find nth centered  ` `# dodecahedral number ` ` `  `# Function to find centered ` `# dodecahedral number ` `def` `CenteredDodecahedral_num(n) : ` `     `  `    ``# Formula to calculate nth ` `    ``# centered dodecahedral number ` `    ``return` `(``2` `*` `n ``+` `1``) ``*` `(``5` `*` `n ``*` `n ``+` `5` `*` `n ``+` `1``) ` ` `  `# Driver Code ` `if` `__name__ ``=``=` `'__main__'` `: ` `         `  `    ``n ``=` `3` `    ``print``(n,``"rd centered dodecahedral number: "``, ` `                ``CenteredDodecahedral_num(n)) ` `    ``n ``=` `10` `    ``print``(n,``"th centered dodecahedral number : "``, ` `                ``CenteredDodecahedral_num(n)) ` `                 `  `# This code is contributed by aj_36 `

C#

 `// C# Program to find  ` `// nth centered ` `// dodecahedral number ` `using` `System; ` ` `  `class` `GFG ` `{ ` `     `  `    ``// Function to find  ` `    ``// nth centered  ` `    ``// dodecahedral number ` `    ``static` `int` `CenteredDodecahedral_num(``int` `n) ` `    ``{ ` `         `  `        ``// Formula to calculate  ` `        ``// nth centered dodecahedral  ` `        ``// number and return it ` `        ``// into main function. ` `        ``return` `(2 * n + 1) *  ` `               ``(5 * n * n +  ` `                ``5 * n + 1); ` `    ``} ` `     `  `    ``// Driver Code ` `    ``static` `public` `void` `Main () ` `    ``{ ` `        ``int` `n = 3; ` `         `  `        ``// print result ` `        ``Console.Write( n + ``"th Centered "` `+  ` `                 ``"Dodecahedral number : "``); ` `        ``Console.WriteLine( ` `                ``CenteredDodecahedral_num(n)); ` ` `  `        ``n = 10; ` `         `  `        ``// print result ` `        ``Console.Write( n + ``"th Centered "` `+  ` `                 ``"Dodecahedral number : "``); ` `        ``Console.WriteLine(  ` `                ``CenteredDodecahedral_num(n)); ` `    ``} ` `} ` ` `  `// This code is contributed by ajit `

PHP

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Output :

```3th Centered Dodecahedral number : 427
10th Centered Dodecahedral number : 11571
```

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