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# Centered dodecahedral number

• Last Updated : 20 Jul, 2021

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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## Javascript

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Output :

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

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

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