Centered heptagonal number

Last Updated : 19 May, 2022

Given a number n, the task is to find n^th 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. N^th 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;
}

// C program to find n-th
// Centered heptagonal number
#include <stdio.h>

// 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;
    printf("%ldth Centered heptagonal number : ",n); 
    printf("%d",centered_heptagonal_num(n));
    return 0;
}

// This code is contributed by kothavvsaakash.

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# 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)

Heptagonal number

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