# Centered tridecagonal number

Given a number n, the task is to find the **nth **Centered Tridecagonal Number.

A **Centered tridecagonal number **represents a dot at the center and other dots surrounding the center dot

in the successive tridecagonal(13 sided polygon) layer.

**Examples :**

Input : 2

Output : 14Input : 9

Output : 469

Formula for nth Centered tridecagonal number:

## C++

`// C++ Program to find nth` `// centered tridecagonal number` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find nth centered` `// tridecagonal number` `int` `centeredTridecagonalNum(` `long` `int` `n)` `{` ` ` `// Formula to calculate nth` ` ` `// centered tridecagonal number` ` ` `return` `(13 * n * (n - 1) + 2) / 2;` `}` `// Drivers code` `int` `main()` `{` ` ` `long` `int` `n = 3;` ` ` `cout << centeredTridecagonalNum(n);` ` ` `cout << endl;` ` ` `n = 10;` ` ` `cout << centeredTridecagonalNum(n);` ` ` `return` `0;` `}` |

## Java

`// Java Program to find nth` `// centered tridecagonal number` `import` `java.io.*;` `class` `GFG` `{` `// Function to find nth centered` `// tridecagonal number` `static` `long` `centeredTridecagonalNum(` `long` `n)` `{` ` ` `// Formula to calculate nth` ` ` `// centered tridecagonal number` ` ` `return` `(` `13` `* n * (n - ` `1` `) + ` `2` `) / ` `2` `;` `}` `// Driver Code` `public` `static` `void` `main (String[] args)` `{` ` ` `long` `n = ` `3` `;` ` ` `System.out.println(centeredTridecagonalNum(n));` ` ` `n = ` `10` `;` ` ` `System.out.println(centeredTridecagonalNum(n));` `}` `}` `// This code is contributed by anuj_67.` |

## Python3

`# Program to find nth centered` `# tridecagonal number` `# Function to find centered` `# tridecagonal number` `def` `centeredTridecagonalNum(n) :` ` ` ` ` `# Formula to calculate nth` ` ` `# centered tridecagonal number` ` ` `return` `(` `13` `*` `n ` `*` ` ` `(n ` `-` `1` `) ` `+` `2` `) ` `/` `/` `2` `# Driver Code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` ` ` `n ` `=` `3` ` ` `print` `(centeredTridecagonalNum(n))` ` ` `n ` `=` `10` ` ` `print` `(centeredTridecagonalNum(n))` ` ` `# This code is contributed` `# by akt_mit` |

## C#

`// C# Program to find nth` `// centered tridecagonal number` `using` `System;` `class` `GFG` `{` `// Function to find nth centered` `// tridecagonal number` `static` `long` `centeredTridecagonalNum(` `long` `n)` `{` ` ` `// Formula to calculate nth` ` ` `// centered tridecagonal number` ` ` `return` `(13 * n * (n - 1) + 2) / 2;` `}` `// Driver Code` `public` `static` `void` `Main ()` `{` ` ` `long` `n = 3;` ` ` `Console.WriteLine(centeredTridecagonalNum(n));` ` ` `n = 10;` ` ` `Console.WriteLine(centeredTridecagonalNum(n));` `}` `}` `// This code is contributed by anuj_67.` |

## PHP

`<?php` `// PHP Program to find nth` `// centered tridecagonal number` `// Function to find nth centered` `// tridecagonal number` `function` `centeredTridecagonalNum( ` `$n` `)` `{` ` ` `// Formula to calculate nth` ` ` `// centered tridecagonal number` ` ` `return` `(13 * ` `$n` `*` ` ` `(` `$n` `- 1) + 2) / 2;` `}` `// Driver Code` `$n` `= 3;` `echo` `centeredTridecagonalNum(` `$n` `);` `echo` `"\n"` `;` `$n` `= 10;` `echo` `centeredTridecagonalNum(` `$n` `);` `// This code is contributed by anuj_67.` `?>` |

## Javascript

`<script>` `// Javascript program to find nth` `// centered tridecagonal number` `// Function to find nth centered` `// tridecagonal number` `function` `centeredTridecagonalNum(n)` `{` ` ` ` ` `// Formula to calculate nth` ` ` `// centered tridecagonal number` ` ` `return` `(13 * n * (n - 1) + 2) / 2;` `}` `// Driver code` `var` `n = 3;` `document.write(centeredTridecagonalNum(n) + ` `"<br>"` `);` ` ` `n = 10;` `document.write(centeredTridecagonalNum(n));` `// This code is contributed by Ankita saini` `</script>` |

**Output :**

40 586

**Time Complexity:** O(1)**Auxiliary Space:** O(1)

Reference: http://oeis.org/wiki/Figurate_numbers

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