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++

[sourcecode language=”CPP”]

// 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;

}

[/sourcecode]

## Java

[sourcecode language=”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.

[/sourcecode]

## C#

[sourcecode language=”CSHARP”]

// 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.

[/sourcecode]

## PHP

[sourcecode language=”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

?>

[/sourcecode]

**Output :**

7th Centered pentagonal number: 106

## Recommended Posts:

- n'th Pentagonal Number
- Pentagonal Pyramidal Number
- Program to check if N is a Pentagonal Number
- Centered Pentadecagonal Number
- Centered hexagonal number
- Centered dodecahedral number
- Centered Hexadecagonal Number
- Centered Octahedral number
- Centered triangular number
- Centered nonadecagonal number
- Centered Octagonal Number
- Centered decagonal number
- Centered cube number
- Centered Octadecagonal Number
- Centered heptagonal number

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