Centered pentagonal number

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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 :

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;
}

C

// 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.

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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