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 N^th 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++

// 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#

// 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:

325

Time Complexity: O(N)

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