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# Find the sum of the first N Centered Octadecagonal Numbers

• Last Updated : 18 Mar, 2021

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

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`

## Javascript

 ``
Output:
`75`

Time Complexity: O(N).

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