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Centered heptagonal number

  • Last Updated : 13 Jul, 2021

Given a number n, the task is to find nth Centered heptagonal number. 
Centered heptagonal number is centered figure number that represents a heptagon with dot in center and all other dot surrounding in heptagonal form. Nth centered heptagonal number can be calculated by using formula (7n2 – 7n + 2) / 2.
Examples :

Input : n = 2
Output : 8

Input : n = 7
Output : 148

Please refer this diagram for pictorial representation.
 

Below is the implementation : 
 

C++




// CPP program to find n-th
// Centered heptagonal number
#include <bits/stdc++.h>
 
using namespace std;
 
// Function to find Centered
// heptagonal number
int centered_heptagonal_num(long int n)
{
    // Formula to calculate nth
    // Centered heptagonal number
    return (7 * n * n - 7 * n + 2) / 2;
}
 
// Driver Code
int main()
{
    long int n = 5;
    cout << n << "th Centered heptagonal number : ";
    cout << centered_heptagonal_num(n);
    return 0;
}

Java




// Java program to find n-th Centered
// heptagonal number
import java.io.*;
 
class GFG {
 
    // Function to find Centered heptagonal
    // number
    static long centered_heptagonal_num(long n)
    {
         
        // Formula to calculate nth
        // Centered heptagonal number
        return (7 * n * n - 7 * n + 2) / 2;
    }
     
    // Driver Code
    public static void main (String[] args)
    {
        long n = 5;
        System.out.println( n + "th Centered "
                      + "heptagonal number : "
                + centered_heptagonal_num(n));
    }
}
 
// This code is contributed by anuj_67.

Python3




# Python program to find nth
# Centered heptagonal number
 
# Function to find Centered
# heptagonal number
def centered_heptagonal_num(n):
 
    # Formula to calculate nth
    # Centered heptagonal number
    return (7 * n * n - 7 * n + 2) // 2
 
 
# Driver Code
n = 5
print("%sth Centered heptagonal number : " %n,
                    centered_heptagonal_num(n))

C#




//C# program to find n-th Centered
// heptagonal number
using System;
 
class GFG {
 
    // Function to find Centered heptagonal
    // number
    static long centered_heptagonal_num(long n)
    {
         
        // Formula to calculate nth
        // Centered heptagonal number
        return (7 * n * n - 7 * n + 2) / 2;
    }
     
    // Driver Code
    public static void Main ()
    {
        long n = 5;
        Console.WriteLine( n + "th Centered "
                    + "heptagonal number : "
                + centered_heptagonal_num(n));
    }
}
 
// This code is contributed by anuj_67.

PHP




<?php
// PHP program to find n-th
// Centered heptagonal number
 
// Function to find Centered
// heptagonal number
function centered_heptagonal_num($n)
{
    // Formula to calculate nth
    // Centered heptagonal number
    return (7 * $n * $n - 7 *
                $n + 2) / 2;
}
 
// Driver Code
$n = 5;
echo $n ,"th Centered heptagonal number : ";
echo centered_heptagonal_num($n);
 
// This code is contributed by m_kit
?>

Javascript




<script>
// Javascript program to find n-th
// Centered heptagonal number
 
// Function to find Centered
// heptagonal number
function centered_heptagonal_num(n)
{
    // Formula to calculate nth
    // Centered heptagonal number
    return parseInt((7 * n * n - 7 * n + 2) / 2);
}
 
// Driver Code
let n = 5;
document.write(n + "th Centered heptagonal number : ");
document.write(centered_heptagonal_num(n));
 
// This code is contributed by rishavmahato348.
</script>

Output : 
 

5th Centered heptagonal number : 71

Time Complexity: O(1)
Auxiliary Space: O(1)
 

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