# Find the sum of the first N Centered Octagonal Number

• Last Updated : 17 Mar, 2021

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 = 3
Output: 35
Explanation:
1, 9 and 25 are the first three Centered Octagonal numbers.
Input: N = 5
Output: 165

Approach:

1. Initially, we need to create a function which will help us to calculate the Nth centered octagonal numbers.
2. Now, run a loop starting from 1 to N, to find ith centered octagonal numbers.
3. Add all the above calculated centered octagonal numbers.
4. 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``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

 `` `// This code is contributed by divyeshrabadiya07.`

Output:

`165`

Time Complexity: O(N).

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