# 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:

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.
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 ``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

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Output:

`325`

Time Complexity: O(N)

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

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