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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 ]
 

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++




// 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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