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# Centered pentagonal number

• Last Updated : 16 Jul, 2021

Given an integer n, find the nth Centered pentagonal number.
A Centered Pentagonal Number is a centered figurate number that represents a pentagon with a dot in the centre and other dots surrounding it in pentagonal layers successively [ Source: Wiki ]

Few Centred pentagonal Number are :
1, 6, 16, 31, 51, 76, 106, 141, 181, 226, 276, 331, 391………………..
Examples :

```Input : 3
Output : 16

Input : 9
Output : 181```

Approach:
Centered pentagonal for n-th term is given by :

Basic implementation of the above approach :

## C++

 `// Program to find nth``// Centered pentagonal number.``#include ``using` `namespace` `std;` `// centered pentagonal number function` `int` `centered_pentagonal_Num(``int` `n)``{``    ``// Formula to calculate nth``    ``// Centered pentagonal number``    ``// and return it into main function.` `    ``return` `(5 * n * n - 5 * n + 2) / 2;``}` `// Driver Code``int` `main()``{``    ``int` `n = 7;``    ``cout << n << ``"th Centered pentagonal number: "``;``    ``cout << centered_pentagonal_Num(n);``    ``return` `0;``}`

## Java

 `// Program to find nth``// Centered pentagonal number``import` `java.io.*;` `class` `GFG``{``    ` `// centered pentagonal``// number function``static` `int` `centered_pentagonal_Num(``int` `n)``{``    ``// Formula to calculate``    ``// nth Centered pentagonal``    ``// number and return it``    ``// into main function.` `    ``return` `(``5` `* n * n - ``5` `* n + ``2``) / ``2``;``}` `// Driver Code``public` `static` `void` `main (String[] args)``{``int` `n = ``7``;``System.out.print(n + ``"th Centered "` `+``              ``"pentagonal number: "``);``System.out.println(centered_pentagonal_Num(n));``}``}` `// This code is contributed by anuj_67.`

## Python3

 `# Python program to find Nth``# Centered pentagonal number.` `# Function to calculate``# Centered pentagonal number.` `def` `centered_pentagonal_Num(n):` `    ``# Formula to calculate nth``    ``# Centered pentagonal number.``    ` `    ``return` `(``5` `*` `n ``*` `n ``-` `5` `*` `n ``+` `2``) ``/``/` `2` `# Driver Code``n ``=` `7``print``(``"%sth Centered pentagonal number : "` `%``n,``                    ``centered_pentagonal_Num(n))``                    ` `# This code is contributed by ajit                `

## C#

 `// C# Program to find nth``// Centered pentagonal number``using` `System;` `class` `GFG``{``    ` `// centered pentagonal``// number function``static` `int` `centered_pentagonal_Num(``int` `n)``{``    ``// Formula to calculate``    ``// nth Centered pentagonal``    ``// number and return it``    ``// into main function.` `    ``return` `(5 * n * n - 5 * n + 2) / 2;``}` `// Driver Code``public` `static` `void` `Main ()``{``int` `n = 7;``Console.Write(n + ``"th Centered "` `+``           ``"pentagonal number: "``);``Console.WriteLine(centered_pentagonal_Num(n));``}``}` `// This code is contributed by anuj_67.`

## PHP

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## Javascript

 ``

Output :

`7th Centered pentagonal number: 106`

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

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