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Find the sum of the first N Centered Decagonal Numbers
• Last Updated : 17 Mar, 2021

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

The first few Centered decagonal numbers are 1, 11, 31, 61, 101, 151 …

Examples:

Input: N = 3
Output: 43
Explanation:
1, 11 and 31 are the first three Centered decagonal numbers.
Input: N = 5
Output: 205

Approach:

1. Initially, we need to create a function which will help us to calculate the Nth Centered decagonal number.
2. Now, run a loop starting from 1 to N, to find the ith Centered decagonal number.
3. Add all the above calculated Centered decagonal numbers.
4. Finally, display the sum of 1st N Centered decagonal numbers.

Below is the implementation of the above approach:

## C++

 `// C++ program to find the sum of the``// first N centred decagonal number``#include ``using` `namespace` `std;` `// Function to find the N-th``// centred decagonal number``int` `Centered_decagonal_num(``int` `n)``{` `    ``// Formula to calculate nth``    ``// centered_decagonal number``    ``// & return it into main function.``    ``return` `(5 * n * n - 5 * n + 1);``}` `// Function to find the sum of``// the first N centered decagonal``// numbers``int` `sum_Centered_decagonal_num(``int` `n)``{` `    ``// Variable to store``    ``// the sum``    ``int` `summ = 0;` `    ``// Iterating through the range``    ``for``(``int` `i = 1; i < n + 1; i++)``    ``{``       ``summ += Centered_decagonal_num(i);``    ``}``    ``return` `summ;``}` `// Driver code``int` `main()``{``    ``int` `n = 5;` `    ``// Display first Nth``    ``// centered_decagonal number``    ``cout << (sum_Centered_decagonal_num(n));` `    ``return` `0;``}` `// This code is contributed by PrinciRaj1992`

## Java

 `// Java program to find the sum of the``// first N centred decagonal number``class` `GFG {``    ` `// Function to find the N-th``// centred decagonal number``static` `int` `Centered_decagonal_num(``int` `n)``{` `    ``// Formula to calculate nth``    ``// centered_decagonal number``    ``// & return it into main function.``    ``return` `(``5` `* n * n - ``5` `* n + ``1``);``}` `// Function to find the sum of``// the first N centered decagonal``// numbers``static` `int` `sum_Centered_decagonal_num(``int` `n)``{` `    ``// Variable to store``    ``// the sum``    ``int` `summ = ``0``;` `    ``// Iterating through the range``    ``for``(``int` `i = ``1``; i < n + ``1``; i++)``    ``{``       ``summ += Centered_decagonal_num(i);``    ``}``    ``return` `summ;``}` `// Driver code``public` `static` `void` `main(String[] args)``{``    ``int` `n = ``5``;` `    ``// Display first Nth``    ``// centered_decagonal number``    ``System.out.println(sum_Centered_decagonal_num(n));``}``}` `// This code is contributed by sapnasingh4991`

## Python3

 `# Python3 program to find the sum of``# the first N centred``# decagonal number` `# Function to find the N-th``# centred decagonal number``def` `Centered_decagonal_num(n):` `    ``# Formula to calculate ``    ``# nth Centered_decagonal``    ``# number & return it``    ``# into main function.``    ``return` `(``5` `*` `n ``*` `n ``-``            ``5` `*` `n ``+` `1``)``    ` `  ` `# Function to find the``# sum of the first N``# Centered decagonal``# numbers``def` `sum_Centered_decagonal_num(n) :``    ` `    ``# Variable to store``    ``# the sum``    ``summ ``=` `0``    ` `    ``# Iterating through the range``    ``for` `i ``in` `range``(``1``, n ``+` `1``):` `        ``summ ``+``=` `Centered_decagonal_num(i)``    ` `    ``return` `summ``  ` `# Driver code``if` `__name__ ``=``=` `'__main__'` `:``          ` `    ``n ``=` `5``    ` `    ``# display first Nth``    ``# Centered_decagonal number``    ``print``(sum_Centered_decagonal_num(n))`

## C#

 `// C# program to find the sum of the``// first N centred decagonal number``using` `System;` `class` `GFG {``    ` `// Function to find the N-th``// centred decagonal number``static` `int` `Centered_decagonal_num(``int` `n)``{` `    ``// Formula to calculate nth``    ``// centered_decagonal number``    ``// & return it into main function.``    ``return` `(5 * n * n - 5 * n + 1);``}` `// Function to find the sum of``// the first N centered decagonal``// numbers``static` `int` `sum_Centered_decagonal_num(``int` `n)``{` `    ``// Variable to store``    ``// the sum``    ``int` `summ = 0;` `    ``// Iterating through the range``    ``for``(``int` `i = 1; i < n + 1; i++)``    ``{``        ``summ += Centered_decagonal_num(i);``    ``}``    ``return` `summ;``}` `// Driver code``public` `static` `void` `Main(String[] args)``{``    ``int` `n = 5;` `    ``// Display first Nth``    ``// centered_decagonal number``    ``Console.WriteLine(sum_Centered_decagonal_num(n));``}``}` `// This code is contributed by sapnasingh4991`

## Javascript

 ``
Output:
`205`

Time Complexity: O(N).

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