# Find the sum of the first N Centered Octadecagonal Numbers

Given a number N, the task is to find the sum of first N Centered Octadecagonal numbers.

Examples:

Input: N = 3
Output: 75
Explanation:
1, 19 and 55 are the first three centered octadecagonal numbers.

Input: N = 10
Output: 298

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:

1. Initially, we need to create a function which will help us to calculate the Nth centered octadecagonal number.
2. Now, run a loop starting from 1 to N, to find ith centered octadecagonal numbers.
4. Finally, display the sum of the first N centered octadecagonal numbers.

Below is the implementation of the above approach:

## C++

 `// C++ program to find the sum of the  ` `// first N centered octadecagonal numbers ` `#include  ` `using` `namespace` `std;  ` ` `  `// Function to find the N-th centered ` `// octadecagonal number ` `int` `center_octadecagon_num(``int` `n) ` `{ ` ` `  `    ``// Formula to calculate ` `    ``// nth centered octadecagonal ` `    ``// number ` `    ``return` `(9 * n * n - 9 * n + 1); ` `} ` ` `  `// Function to find the sum of the first ` `// N centered octadecagonal numbers ` `int` `sum_center_octadecagon_num(``int` `n) ` `{ ` ` `  `    ``// Variable to store ` `    ``// the sum ` `    ``int` `summ = 0; ` ` `  `    ``// Iterating through the range ` `    ``// 1 to N ` `    ``for``(``int` `i = 1; i < n + 1; i++) ` `    ``{ ` `        ``summ += center_octadecagon_num(i); ` `    ``} ` `    ``return` `summ; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``int` `n = 3; ` ` `  `    ``cout << (sum_center_octadecagon_num(n)); ` `    ``return` `0; ` `} ` ` `  `// This code is contributed by Rajput-Ji `

## Java

 `// Java program to find the sum of the   ` `// first N centered octadecagonal numbers ` `class` `GFG { ` `     `  `// Function to find the N-th centered ` `// octadecagonal number ` `static` `int` `center_octadecagon_num(``int` `n) ` `{ ` ` `  `    ``// Formula to calculate ` `    ``// nth centered octadecagonal ` `    ``// number ` `    ``return` `(``9` `* n * n - ``9` `* n + ``1``); ` `} ` ` `  `// Function to find the sum of the first ` `// N centered octadecagonal numbers ` `static` `int` `sum_center_octadecagon_num(``int` `n) ` `{ ` ` `  `    ``// Variable to store ` `    ``// the sum ` `    ``int` `summ = ``0``; ` ` `  `    ``// Iterating through the range ` `    ``// 1 to N ` `    ``for``(``int` `i = ``1``; i < n + ``1``; i++) ` `    ``{ ` `       ``summ += center_octadecagon_num(i); ` `    ``} ` `    ``return` `summ; ` `} ` ` `  `// Driver Code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `n = ``3``; ` ` `  `    ``System.out.println(sum_center_octadecagon_num(n)); ` `} ` `} ` ` `  `// This code is contributed by sapnasingh4991 `

## Python3

 `# Python3 program to find the sum of  ` `# the first N Centered Octadecagonal  ` `# numbers ` ` `  `# Function to find the N-th ` `# Centered octadecagonal  ` `# number  ` `def` `center_octadecagon_num(n):  ` ` `  `    ``# Formula to calculate   ` `    ``# nth centered octadecagonal  ` `    ``# number ` `    ``return` `(``9` `*` `n ``*` `n ``-` `9` `*` `n ``+` `1``) ` `     `  `   `  `# Function to find the sum of  ` `# the first N Centered  ` `# octadecagonal numbers ` `def` `sum_center_octadecagon_num(n) :  ` `     `  `    ``# Variable to store  ` `    ``# the sum ` `    ``summ ``=` `0` `     `  `    ``# Iterating through the range  ` `    ``# 1 to N ` `    ``for` `i ``in` `range``(``1``, n ``+` `1``): ` ` `  `        ``summ ``+``=` `center_octadecagon_num(i) ` `     `  `    ``return` `summ ` `   `  `# Driver code  ` `if` `__name__ ``=``=` `'__main__'` `:  ` `           `  `    ``n ``=` `3` `     `  `    ``print``(sum_center_octadecagon_num(n))  `

## C#

 `// C# program to find the sum of the  ` `// first N centered octadecagonal numbers ` `using` `System; ` ` `  `class` `GFG { ` `     `  `// Function to find the N-th centered ` `// octadecagonal number ` `static` `int` `center_octadecagon_num(``int` `n) ` `{ ` ` `  `    ``// Formula to calculate ` `    ``// nth centered octadecagonal ` `    ``// number ` `    ``return` `(9 * n * n - 9 * n + 1); ` `} ` ` `  `// Function to find the sum of the first ` `// N centered octadecagonal numbers ` `static` `int` `sum_center_octadecagon_num(``int` `n) ` `{ ` ` `  `    ``// Variable to store ` `    ``// the sum ` `    ``int` `summ = 0; ` ` `  `    ``// Iterating through the range ` `    ``// 1 to N ` `    ``for``(``int` `i = 1; i < n + 1; i++) ` `    ``{ ` `        ``summ += center_octadecagon_num(i); ` `    ``} ` `    ``return` `summ; ` `} ` ` `  `// Driver Code ` `public` `static` `void` `Main(String[] args) ` `{ ` `    ``int` `n = 3; ` ` `  `    ``Console.WriteLine(sum_center_octadecagon_num(n)); ` `} ` `} ` ` `  `// This code is contributed by sapnasingh4991 `

Output:

```75
```

Time Complexity: O(N).

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Improved By : sapnasingh4991, Rajput-Ji

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