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++

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// 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;
}

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Java

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// 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.

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Python3

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# 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                 

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C#

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// 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.

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PHP

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<?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
?>

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Output :

7th Centered pentagonal number: 106


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