# Find the sum of the first N Centered Octagonal Number

Given a number N, the task is to find the sum of the first N Centered Octagonal Numbers.

The first few Centered Octagonal numbers are

1, 9, 25, 49, 81, 121, 169, 225, 289, 361 …

**Examples:**

Input:N = 3Output:35Explanation:

1, 9 and 25 are the first three Centered Octagonal numbers.Input:N = 5Output:165

**Approach:**

- Initially, we need to create a function which will help us to calculate the N
^{th}centered octagonal numbers. - Now, run a loop starting from 1 to N, to find i
^{th}centered octagonal numbers. - Add all the above calculated centered octagonal numbers.
- Finally, display the sum of the first N centered octagonal numbers.

Below is the implementation of the above approach:

## C++

`// C++ program to find the sum of the` `// first N centered octagonal number` `#include<bits/stdc++.h>` `using` `namespace` `std;` `// Function to find the N-th centered` `// octagonal number` `int` `center_Octagonal_num(` `int` `n)` `{` ` ` `// Formula to calculate` ` ` `// nth centered octagonal` ` ` `// number` ` ` `return` `(4 * n * n - 4 * n + 1);` `}` `// Function to find the sum of the first` `// N centered octagonal numbers` `int` `sum_center_Octagonal_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_Octagonal_num(i);` ` ` `}` ` ` `return` `summ;` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `n = 5;` ` ` `cout << (sum_center_Octagonal_num(n));` ` ` `return` `0;` `}` `// This code is contributed by PratikBasu` |

## Java

`// Java program to find the sum of the` `// first N centered octagonal number` `class` `GFG {` ` ` `// Function to find N-th centered` `// octagonal number` `static` `int` `center_Octagonal_num(` `int` `n)` `{` ` ` `// Formula to calculate` ` ` `// nth centered octagonal` ` ` `// number` ` ` `return` `(` `4` `* n * n - ` `4` `* n + ` `1` `);` `}` `// Function to find the` `// sum of the first N` `// centered octagonal` `// numbers` `static` `int` `sum_center_Octagonal_num(` `int` `n)` `{` ` ` `// Variable to store` ` ` `// the sum` ` ` `int` `summ = ` `0` `;` ` ` `// Iterating through the first N` ` ` `// numbers` ` ` `for` `(` `int` `i = ` `1` `; i < n + ` `1` `; i++)` ` ` `{` ` ` `summ += center_Octagonal_num(i);` ` ` `}` ` ` `return` `summ;` `}` `// Driver code` `public` `static` `void` `main(String[] args)` `{` ` ` `int` `n = ` `5` `;` ` ` `System.out.println(sum_center_Octagonal_num(n));` `}` `}` `// This code is contributed by Princi Singh` |

## Python3

`# Python3 program to find the` `# sum of the first N` `# Centered Octagonal number` `# Function to find N-th` `# Centered Octagonal` `# number` `def` `center_Octagonal_num(n):` ` ` `# Formula to calculate ` ` ` `# nth centered Octagonal` ` ` `# number` ` ` `return` `(` `4` `*` `n ` `*` `n ` `-` `4` `*` `n ` `+` `1` `)` ` ` ` ` `# Function to find the` `# sum of the first N` `# Centered Octagonal` `# numbers` `def` `sum_center_Octagonal_num(n) :` ` ` ` ` `# Variable to store` ` ` `# the sum` ` ` `summ ` `=` `0` ` ` ` ` `# Iterating through the first N` ` ` `# numbers` ` ` `for` `i ` `in` `range` `(` `1` `, n ` `+` `1` `):` ` ` `summ ` `+` `=` `center_Octagonal_num(i)` ` ` ` ` `return` `summ` ` ` `# Driver code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` ` ` `n ` `=` `5` ` ` ` ` `print` `(sum_center_Octagonal_num(n))` |

## C#

`// C# program to find the sum of the` `// first N centered octagonal number` `using` `System;` `class` `GFG{` ` ` `// Function to find N-th centered` `// octagonal number` `static` `int` `center_Octagonal_num(` `int` `n)` `{` ` ` `// Formula to calculate` ` ` `// nth centered octagonal` ` ` `// number` ` ` `return` `(4 * n * n - 4 * n + 1);` `}` `// Function to find the sum of` `// the first N centered octagonal` `// numbers` `static` `int` `sum_center_Octagonal_num(` `int` `n)` `{` ` ` `// Variable to store` ` ` `// the sum` ` ` `int` `summ = 0;` ` ` `// Iterating through the first N` ` ` `// numbers` ` ` `for` `(` `int` `i = 1; i < n + 1; i++)` ` ` `{` ` ` `summ += center_Octagonal_num(i);` ` ` `}` ` ` `return` `summ;` `}` `// Driver code` `public` `static` `void` `Main()` `{` ` ` `int` `n = 5;` ` ` `Console.WriteLine(sum_center_Octagonal_num(n));` `}` `}` `// This code is contributed by Akanksha_Rai` |

## Javascript

`<script>` ` ` `// Javascript program to find the sum of the ` ` ` `// first N centered octagonal number` ` ` ` ` `// Function to find the N-th centered` ` ` `// octagonal number ` ` ` `function` `center_Octagonal_num(n)` ` ` `{` ` ` `// Formula to calculate` ` ` `// nth centered octagonal ` ` ` `// number` ` ` `return` `(4 * n * n - 4 * n + 1);` ` ` `}` ` ` `// Function to find the sum of the first` ` ` `// N centered octagonal numbers` ` ` `function` `sum_center_Octagonal_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_Octagonal_num(i);` ` ` `}` ` ` `return` `summ;` ` ` `}` ` ` ` ` `let n = 5;` ` ` ` ` `document.write(sum_center_Octagonal_num(n));` `</script>` `// This code is contributed by divyeshrabadiya07.` |

**Output:**

165

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

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