# Centered pentagonal number

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 <bits/stdc++.h>` `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

`<?php` `// PHP Program to find nth` `// Centered pentagonal number.` `// Centered pentagonal number function` `function` `centered_pentagonal_Num(` `$n` `)` `{` ` ` `// Formula to calculate nth` ` ` `// Centered pentagonal number` ` ` `// and return it into main function.` ` ` `return` `(5 * ` `$n` `* ` `$n` `- 5 * ` `$n` `+ 2) / 2;` `}` `// Driver Code` `$n` `= 7;` `echo` `$n` `, ` `"th Centered pentagonal number: "` `;` `echo` `centered_pentagonal_Num(` `$n` `);` `// This code is contributed by aj_36` `?>` |

## Javascript

`<script>` `// Program to find nth` `// Centered pentagonal number` ` ` `// centered pentagonal` `// number function` `function` `centered_pentagonal_Num(n)` `{` ` ` `// Formula to calculate` ` ` `// nth Centered pentagonal` ` ` `// number and return it` ` ` `// into main function.` ` ` `return` `(5 * n * n - 5 * n + 2) / 2;` `}` `// Driver Code` `var` `n = 7;` `document.write(n + ` `"th Centered "` `+` ` ` `"pentagonal number: "` `);` `document.write(centered_pentagonal_Num(n));` `// This code is contributed by Amit Katiyar` `</script>` |

**Output :**

7th Centered pentagonal number: 106

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

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