Find the sum of the first Nth Centered Hexadecagonal Number

Given a number N, the task is to find the sum of the first N Centered Hexadecagonal Number.

The first few Centered Hexadecagonal Numbers are 1, 17, 49, 97, 161, 241 …

Examples:

Input: N = 3
Output: 67
Explanation:
1, 17 and 49 are the first three centered Hexadecagonal numbers.

Input: N = 5
Output: 325



Approach:

  1. Initially, we need to create a function which will help us to calculate the Nth Centered Hexadecagonal number.
  2. Now, we run a loop starting from 1 to N, to find ith Centered Hexadecagonal number.
  3. Add all the above calculated Centered Hexadecagonal numbers.
  4. Finally, display the sum of 1st N Centered Hexadecagonal numbers.

Below is the implementation of the above approach:

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ program to find the sum of the first 
// N centred hexadecagonal numbers
#include <bits/stdc++.h> 
using namespace std; 
  
// Centered_Hexadecagonal 
// number function
int Centered_Hexadecagonal_num(int n) 
{
      
    // Formula to calculate nth 
    // Centered_Hexadecagonal 
    // number & return it into
    // main function. 
    return (8 * n * n - 8 * n + 1);
}
  
// Function to find the sum of the first
// N centered hexadecagonal number
int sum_Centered_Hexadecagonal_num(int n)
{
      
    // Variable to store the sum
    int summ = 0;
      
    // Loop to iterate through the
    // first N numbers
    for(int i = 1; i < n + 1; i++)
    {
          
       // Finding the sum
       summ += Centered_Hexadecagonal_num(i);
    }
    return summ;
}
  
// Driver code 
int main() 
    int n = 5;
      
    // Display first Nth 
    // Centered_Hexadecagonal number
    cout << sum_Centered_Hexadecagonal_num(n);
  
// This code is contributed by coder001

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java program to find the sum of the first 
// N centred hexadecagonal numbers 
  
class GFG{
      
// Centered_Hexadecagonal 
// number function 
public static int Centered_Hexadecagonal_num(int n) 
          
    // Formula to calculate nth 
    // Centered_Hexadecagonal 
    // number & return it into 
    // main function. 
    return (8 * n * n - 8 * n + 1); 
      
// Function to find the sum of the first 
// N centered hexadecagonal number 
public static int sum_Centered_Hexadecagonal_num(int n) 
          
    // Variable to store the sum 
    int summ = 0
          
    // Loop to iterate through the 
    // first N numbers 
    for(int i = 1; i < n + 1; i++) 
    
          
       // Finding the sum 
       summ += Centered_Hexadecagonal_num(i); 
    
    return summ; 
  
// Driver Code    
public static void main(String[] args)
{
    int n = 5
      
    // Display first Nth 
    // Centered_Hexadecagonal number 
    System.out.println(sum_Centered_Hexadecagonal_num(n));
}
}
  
// This code is contributed by divyeshrabadiya07

chevron_right


Python3

filter_none

edit
close

play_arrow

link
brightness_4
code

# Python3 program to find the sum of 
# the first N centred 
# hexadecagonal numbers
  
# Centered_Hexadecagonal 
# number function
def Centered_Hexadecagonal_num(n): 
    # Formula to calculate  
    # nth Centered_Hexadecagonal 
    # number & return it 
    # into main function. 
    return (8 * n * n - 
            8 * n + 1)
      
    
# Function to find the 
# sum of the first N
# Centered Hexadecagonal 
# number 
def sum_Centered_Hexadecagonal_num(n) : 
      
    # Variable to store the 
    # sum
    summ = 0
      
    # Loop to iterate through the 
    # first N numbers
    for i in range(1, n + 1):
  
        # Find the sum
        summ += Centered_Hexadecagonal_num(i)
      
    return summ
    
# Driver Code 
if __name__ == '__main__'
            
    n = 5
      
    # display first Nth 
    # Centered_Hexadecagonal number
    print(sum_Centered_Hexadecagonal_num(n)) 

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# program to find the sum of the first 
// N centred hexadecagonal numbers 
using System;
  
class GFG{
      
// Centered_Hexadecagonal 
// number function 
public static int Centered_Hexadecagonal_num(int n) 
          
    // Formula to calculate nth 
    // Centered_Hexadecagonal 
    // number & return it into 
    // main function. 
    return (8 * n * n - 8 * n + 1); 
      
// Function to find the sum of the first 
// N centered hexadecagonal number 
public static int sum_Centered_Hexadecagonal_num(int n) 
          
    // Variable to store the sum 
    int summ = 0; 
          
    // Loop to iterate through the 
    // first N numbers 
    for(int i = 1; i < n + 1; i++) 
    
         
       // Finding the sum 
       summ += Centered_Hexadecagonal_num(i); 
    
    return summ; 
  
// Driver Code 
public static void Main()
{
    int n = 5; 
      
    // Display first Nth 
    // Centered_Hexadecagonal number 
    Console.Write(sum_Centered_Hexadecagonal_num(n));
}
}
  
// This code is contributed by Code_Mech

chevron_right


Output:

325

Time Complexity: O(N)

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.




My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.



Article Tags :
Practice Tags :


Be the First to upvote.


Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.