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 center and other dots surrounding it in pentagonal layers successively [ Source: Wiki ]

Few Centered 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 : 

// 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;
}

// C Program to find nth
// Centered pentagonal number.
#include <stdio.h>

// 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;
    printf("%dth Centered pentagonal number: ",n);
    printf("%d",centered_pentagonal_Num(n));
    return 0;
}

// This code is contributed by kothavvsaakash.

// 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.

# 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# 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 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
?>

<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)