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 ]

Centered pentagonal number

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 :

  Cp_{n}=(5n^2-5n+2)/2 

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


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