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 = 3Output:43Explanation:

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

**Approach:**

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

`<script>` ` ` `// Javascript program to find the sum of the ` ` ` `// first N centred decagonal number` ` ` ` ` `// Function to find the N-th` ` ` `// centred decagonal number` ` ` `function` `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` ` ` `function` `sum_Centered_decagonal_num(n)` ` ` `{` ` ` `// Variable to store` ` ` `// the sum` ` ` `let summ = 0;` ` ` `// Iterating through the range` ` ` `for` `(let i = 1; i < n + 1; i++)` ` ` `{` ` ` `summ += Centered_decagonal_num(i);` ` ` `}` ` ` `return` `summ;` ` ` `}` ` ` ` ` `let n = 5;` ` ` ` ` `// Display first Nth ` ` ` `// centered_decagonal number` ` ` `document.write(sum_Centered_decagonal_num(n));` `</script>` |

**Output:**

205

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

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