# 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.
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

 ``

Output:

`325`

Time Complexity: O(N)

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

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