# Find the sum of the first N Centered Dodecagonal Number

Given a number N, the task is to find the sum of first N Centered Dodecagonal Number.

The first few Centered Dodecagonal Numbers are

1, 13, 37, 73, 121, 181 …

**Examples:**

Input:N = 3Output:51Explanation:

1, 13 and 37 are the first three centered Dodecagonal number.Input:N = 5Output:245

**Approach:**

- Initially, create a function which will help us to calculate the N
^{th}Centered Dodecagonal number. - Run a loop starting from 1 to N, to find i-th Centered Dodecagonal number.
- Add all the above calculated Centered Dodecagonal numbers.
- Finally, display the sum of the first N Centered Dodecagonal numbers.

Below is the implementation of the above approach:

## C++

`// C++ program to find the sum` `// of the first N Centred` `// Dodecagonal number` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find the N-th ` `// Centered Dodecagonal number` `int` `Centered_Dodecagonal_num(` `int` `n)` `{` ` ` ` ` `// Formula to calculate nth ` ` ` `// Centered_Dodecagonal number` ` ` `return` `6 * n * (n - 1) + 1;` `}` `// Function to find the sum of the first` `// N Centered_Dodecagonal number` `int` `sum_Centered_Dodecagonal_num(` `int` `n)` `{` ` ` ` ` `// Variable to store the sum` ` ` `int` `summ = 0;` ` ` ` ` `// Iterating from 1 to N` ` ` `for` `(` `int` `i = 1; i < n + 1; i++)` ` ` `{` ` ` `// Finding the sum` ` ` `summ += Centered_Dodecagonal_num(i);` ` ` `}` ` ` `return` `summ;` `}` `// Driver code` `int` `main()` `{` ` ` `int` `n = 5;` ` ` ` ` `cout << sum_Centered_Dodecagonal_num(n);` `}` `// This code is contributed by coder001` |

## Java

`// Java program to find the sum of the ` `// first N centred dodecagonal number` `class` `GFG {` ` ` `// Function to find the N-th` `// centered dodecagonal number` `static` `int` `Centered_Dodecagonal_num(` `int` `n)` `{` ` ` ` ` `// Formula to calculate nth` ` ` `// Centered_Dodecagonal number` ` ` `return` `6` `* n * (n - ` `1` `) + ` `1` `;` `}` ` ` `// Function to find the sum of the first` `// N Centered_Dodecagonal number` `static` `int` `sum_Centered_Dodecagonal_num(` `int` `n)` `{` ` ` ` ` `// Variable to store the sum` ` ` `int` `summ = ` `0` `;` ` ` ` ` `// Iterating from 1 to N` ` ` `for` `(` `int` `i = ` `1` `; i < n + ` `1` `; i++)` ` ` `{` ` ` ` ` `// Finding the sum` ` ` `summ += Centered_Dodecagonal_num(i);` ` ` `}` ` ` `return` `summ;` `}` ` ` `// Driver code` `public` `static` `void` `main (String[] args)` `{` ` ` `int` `n = ` `5` `;` ` ` ` ` `System.out.print(sum_Centered_Dodecagonal_num(n));` `}` `}` `// This code is contributed by AnkitRai01` |

## Python3

`# Python3 program to find the sum` `# of the first N centred` `# Dodecagonal number` `# Function to find the` `# N-th Centered Dodecagonal` `# number` `def` `Centered_Dodecagonal_num(n):` ` ` `# Formula to calculate ` ` ` `# nth Centered_Dodecagonal` ` ` `# number` ` ` `return` `6` `*` `n ` `*` `(n ` `-` `1` `) ` `+` `1` ` ` ` ` `# Function to find the` `# sum of the first N` `# Centered_Dodecagonal` `# number` `def` `sum_Centered_Dodecagonal_num(n) :` ` ` ` ` `# Variable to store the` ` ` `# sum` ` ` `summ ` `=` `0` ` ` ` ` `# Iterating from 1 to N` ` ` `for` `i ` `in` `range` `(` `1` `, n ` `+` `1` `):` ` ` `# Finding the sum` ` ` `summ ` `+` `=` `Centered_Dodecagonal_num(i)` ` ` ` ` `return` `summ` ` ` `# Driver code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` ` ` `n ` `=` `5` ` ` ` ` `print` `(sum_Centered_Dodecagonal_num(n))` |

## C#

`// C# program to find the sum of the` `// first N centred dodecagonal number` `using` `System;` `class` `GFG{` ` ` `// Function to find the N-th` `// centered dodecagonal number` `static` `int` `Centered_Dodecagonal_num(` `int` `n)` `{` ` ` ` ` `// Formula to calculate nth` ` ` `// Centered_Dodecagonal number` ` ` `return` `6 * n * (n - 1) + 1;` `}` ` ` `// Function to find the sum of the first` `// N Centered_Dodecagonal number` `static` `int` `sum_Centered_Dodecagonal_num(` `int` `n)` `{` ` ` ` ` `// Variable to store the sum` ` ` `int` `summ = 0;` ` ` ` ` `// Iterating from 1 to N` ` ` `for` `(` `int` `i = 1; i < n + 1; i++)` ` ` `{` ` ` ` ` `// Finding the sum` ` ` `summ += Centered_Dodecagonal_num(i);` ` ` `}` ` ` `return` `summ;` `}` ` ` `// Driver code` `public` `static` `void` `Main()` `{` ` ` `int` `n = 5;` ` ` ` ` `Console.Write(sum_Centered_Dodecagonal_num(n));` `}` `}` `// This code is contributed by Code_Mech` |

## Javascript

`<script>` ` ` `// Javascript program to find the sum ` ` ` `// of the first N Centred` ` ` `// Dodecagonal number` ` ` ` ` `// Function to find the N-th ` ` ` `// Centered Dodecagonal number ` ` ` `function` `Centered_Dodecagonal_num(n) ` ` ` `{` ` ` `// Formula to calculate nth ` ` ` `// Centered_Dodecagonal number` ` ` `return` `6 * n * (n - 1) + 1;` ` ` `}` ` ` `// Function to find the sum of the first ` ` ` `// N Centered_Dodecagonal number` ` ` `function` `sum_Centered_Dodecagonal_num(n)` ` ` `{` ` ` `// Variable to store the sum` ` ` `let summ = 0;` ` ` `// Iterating from 1 to N` ` ` `for` `(let i = 1; i < n + 1; i++)` ` ` `{` ` ` `// Finding the sum` ` ` `summ += Centered_Dodecagonal_num(i);` ` ` `}` ` ` `return` `summ;` ` ` `}` ` ` ` ` `let n = 5;` ` ` ` ` `document.write(sum_Centered_Dodecagonal_num(n));` `</script>` |

**Output:**

245

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

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