Find the sum of the first Nth Centered Hexadecagonal Number

Last Updated : 18 Mar, 2021

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 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

Java

// 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

Python3

# 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))

C#

// 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

Javascript

<script>
  // Javascript program to find the sum of the first 
  // N centred 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)

Attention reader! Don’t stop learning now. Get hold of all the important mathematical concepts for competitive programming with the Essential Maths for CP Course at a student-friendly price. To complete your preparation from learning a language to DS Algo and many more, please refer Complete Interview Preparation Course.

My Personal Notes

Related Articles

C++

Java

Python3

C#

Javascript