# Centered heptagonal number

Given a number** n**, the task is to find n^{th} Centered heptagonal number.

Centered heptagonal number is centered figure number that represents a heptagon with dot in center and all other dot surrounding in heptagonal form. N^{th} centered heptagonal number can be calculated by using formula **(7n ^{2} – 7n + 2) / 2**.

**Examples :**

Input : n = 2 Output : 8 Input : n = 7 Output : 148

Please refer this diagram for pictorial representation.

Below is the implementation :

## C++

`// CPP program to find n-th` `// Centered heptagonal number` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find Centered` `// heptagonal number` `int` `centered_heptagonal_num(` `long` `int` `n)` `{` ` ` `// Formula to calculate nth` ` ` `// Centered heptagonal number` ` ` `return` `(7 * n * n - 7 * n + 2) / 2;` `}` `// Driver Code` `int` `main()` `{` ` ` `long` `int` `n = 5;` ` ` `cout << n << ` `"th Centered heptagonal number : "` `;` ` ` `cout << centered_heptagonal_num(n);` ` ` `return` `0;` `}` |

## Java

`// Java program to find n-th Centered` `// heptagonal number` `import` `java.io.*;` `class` `GFG {` ` ` `// Function to find Centered heptagonal` ` ` `// number` ` ` `static` `long` `centered_heptagonal_num(` `long` `n)` ` ` `{` ` ` ` ` `// Formula to calculate nth` ` ` `// Centered heptagonal number` ` ` `return` `(` `7` `* n * n - ` `7` `* n + ` `2` `) / ` `2` `;` ` ` `}` ` ` ` ` `// Driver Code` ` ` `public` `static` `void` `main (String[] args)` ` ` `{` ` ` `long` `n = ` `5` `;` ` ` `System.out.println( n + ` `"th Centered "` ` ` `+ ` `"heptagonal number : "` ` ` `+ centered_heptagonal_num(n));` ` ` `}` `}` `// This code is contributed by anuj_67.` |

## Python3

`# Python program to find nth` `# Centered heptagonal number` `# Function to find Centered` `# heptagonal number` `def` `centered_heptagonal_num(n):` ` ` `# Formula to calculate nth` ` ` `# Centered heptagonal number` ` ` `return` `(` `7` `*` `n ` `*` `n ` `-` `7` `*` `n ` `+` `2` `) ` `/` `/` `2` `# Driver Code` `n ` `=` `5` `print` `(` `"%sth Centered heptagonal number : "` `%` `n,` ` ` `centered_heptagonal_num(n))` |

## C#

`//C# program to find n-th Centered` `// heptagonal number` `using` `System;` `class` `GFG {` ` ` `// Function to find Centered heptagonal` ` ` `// number` ` ` `static` `long` `centered_heptagonal_num(` `long` `n)` ` ` `{` ` ` ` ` `// Formula to calculate nth` ` ` `// Centered heptagonal number` ` ` `return` `(7 * n * n - 7 * n + 2) / 2;` ` ` `}` ` ` ` ` `// Driver Code` ` ` `public` `static` `void` `Main ()` ` ` `{` ` ` `long` `n = 5;` ` ` `Console.WriteLine( n + ` `"th Centered "` ` ` `+ ` `"heptagonal number : "` ` ` `+ centered_heptagonal_num(n));` ` ` `}` `}` `// This code is contributed by anuj_67.` |

## PHP

`<?php` `// PHP program to find n-th` `// Centered heptagonal number` `// Function to find Centered` `// heptagonal number` `function` `centered_heptagonal_num(` `$n` `)` `{` ` ` `// Formula to calculate nth` ` ` `// Centered heptagonal number` ` ` `return` `(7 * ` `$n` `* ` `$n` `- 7 *` ` ` `$n` `+ 2) / 2;` `}` `// Driver Code` `$n` `= 5;` `echo` `$n` `,` `"th Centered heptagonal number : "` `;` `echo` `centered_heptagonal_num(` `$n` `);` `// This code is contributed by m_kit` `?>` |

## Javascript

`<script>` `// Javascript program to find n-th` `// Centered heptagonal number` `// Function to find Centered` `// heptagonal number` `function` `centered_heptagonal_num(n)` `{` ` ` `// Formula to calculate nth` ` ` `// Centered heptagonal number` ` ` `return` `parseInt((7 * n * n - 7 * n + 2) / 2);` `}` `// Driver Code` `let n = 5;` `document.write(n + ` `"th Centered heptagonal number : "` `);` `document.write(centered_heptagonal_num(n));` `// This code is contributed by rishavmahato348.` `</script>` |

**Output :**

5th Centered heptagonal number : 71

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

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