# 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 = 3Output:75Explanation:

1, 19 and 55 are the first three centered octadecagonal numbers.Input:N = 10Output:298

**Approach:**

- Initially, we need to create a function which will help us to calculate the N
^{th}centered octadecagonal number. - Now, run a loop starting from 1 to N, to find i
^{th}centered octadecagonal numbers. - Add all the above calculated centered octadecagonal numbers.
- 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<bits/stdc++.h>` `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

`<script>` ` ` `// Javascript program to find the sum of the ` ` ` `// first N centered octadecagonal numbers` ` ` ` ` `// Function to find the N-th centered` ` ` `// octadecagonal number` ` ` `function` `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` ` ` `function` `sum_center_octadecagon_num(n)` ` ` `{` ` ` `// Variable to store` ` ` `// the sum` ` ` `let summ = 0;` ` ` `// Iterating through the range` ` ` `// 1 to N` ` ` `for` `(let i = 1; i < n + 1; i++)` ` ` `{` ` ` `summ += center_octadecagon_num(i);` ` ` `}` ` ` `return` `summ;` ` ` `}` ` ` ` ` `let n = 3;` ` ` `document.write(sum_center_octadecagon_num(n));` `// This code is contributed by divyeshrabadiya07.` `</script>` |

**Output:**

75

**Time Complexity:** O(N).

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