Find the sum of the first Nth Centered Hexadecagonal Number

Last Updated : 19 Sep, 2022

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:

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

Below is the implementation of the above approach:

C++

// C++ program to find the sum of the first 
// N centered 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

Java

// Java program to find the sum of the first 
// N centered 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

Python3

# Python3 program to find the sum of 
# the first N centered 
# 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))

// C# program to find the sum of the first 
// N centered 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

JavaScript

<script>
  // Javascript program to find the sum of the first  
  // N centered hexadecagonal numbers 
  
  // Centered_Hexadecagonal  
  // number function 
  function 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 
  function sum_Centered_Hexadecagonal_num(n) 
  { 

      // Variable to store the sum 
      let summ = 0; 

      // Loop to iterate through the 
      // first N numbers 
      for(let i = 1; i < n + 1; i++) 
      { 

         // Finding the sum 
         summ += Centered_Hexadecagonal_num(i); 
      } 
      return summ; 
  }
  
  let n = 5; 
      
  // Display first Nth  
  // Centered_Hexadecagonal number 
  document.write(sum_Centered_Hexadecagonal_num(n)); 
  
  // This code is contributed by divyesh072019.
</script>

Output:

Time Complexity: O(N)

Auxiliary Space: O(1) as it is using constant space for variables

Find the sum of the first Nth Centered Hexadecagonal Number

SHUBHAMSINGH10

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Find the sum of the first Nth Centered Hexadecagonal Number

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