We are given a number n, we need to find n-th centered Icosahedral number.**Description:** A centered icosahedral number is a centered figurate number that represents an icosahedron.**The first few centered icosahedral number** series are :

1, 13, 55, 147, 309, 561, 923, 1415, 2057, 2869, 3871, 5083, 6525, 8217……………….

Mathematical Formula for **nth** Centered icosahedral number:

**Examples :**

Input : n = 4 Output : 309 Input : n = 12 Output : 6525

Below is the implementation of the above formula

## C++

`// C++ Program to find nth` `// Centered icosahedral number` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find` `// Centered icosahedral number` `int` `centeredIcosahedralNum(` `int` `n)` `{` ` ` `// Formula to calculate nth` ` ` `// Centered icosahedral number` ` ` `// and return it into main function.` ` ` `return` `(2 * n + 1) * (5 * n * n + 5 * n + 3) / 3;` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `n = 10;` ` ` `cout << centeredIcosahedralNum(n) << endl;` ` ` `n = 12;` ` ` `cout << centeredIcosahedralNum(n) << endl;` ` ` `return` `0;` `}` |

## Java

`// Java Program to find nth` `// Centered icosahedral number` `// Java Program to find nth Centered` `// icosahedral number` `import` `java.io.*;` `class` `GFG {` ` ` ` ` `// Function to find Centered` ` ` `// icosahedral number` ` ` `static` `int` `centeredIcosahedralNum(` `int` `n)` ` ` `{` ` ` ` ` `// Formula to calculate nth Centered` ` ` `// icosahedral number and return it` ` ` `// into main function.` ` ` `return` `(` `2` `* n + ` `1` `) * (` `5` `* n * n +` ` ` `5` `* n + ` `3` `) / ` `3` `;` ` ` `}` ` ` ` ` `// Driver Code` ` ` `public` `static` `void` `main (String[] args)` ` ` `{` ` ` `int` `n = ` `10` `;` ` ` `System.out.println(` ` ` `centeredIcosahedralNum(n));` ` ` ` ` `n = ` `12` `;` ` ` `System.out.println(` ` ` `centeredIcosahedralNum(n));` ` ` `}` `}` `// This code is contributed by anuj_67.` |

## Python3

`# Python program to find nth` `# Centered icosahedral number` `# Function to calculate` `# Centered icosahedral number` `def` `centeredIcosahedralNum(n):` ` ` `# Formula to calculate nth` ` ` `# Centered icosahedral number` ` ` `return` `((` `2` `*` `n ` `+` `1` `) ` `*` ` ` `(` `5` `*` `n ` `*` `n ` `+` `5` `*` `n ` `+` `3` `) ` `/` `/` `3` `)` `# Driver Code` `n ` `=` `10` `print` `(centeredIcosahedralNum(n))` `n ` `=` `12` `print` `(centeredIcosahedralNum(n))` ` ` `# This code is contributed by ajit. ` |

## C#

`// C# Program to find nth` `// Centered icosahedral number` `// Java Program to find nth Centered` `// icosahedral number` `using` `System;` `class` `GFG {` ` ` ` ` `// Function to find Centered` ` ` `// icosahedral number` ` ` `static` `int` `centeredIcosahedralNum(` `int` `n)` ` ` `{` ` ` ` ` `// Formula to calculate nth Centered` ` ` `// icosahedral number and return it` ` ` `// into main function.` ` ` `return` `(2 * n + 1) * (5 * n * n +` ` ` `5 * n + 3) / 3;` ` ` `}` ` ` ` ` `// Driver Code` ` ` `public` `static` `void` `Main ()` ` ` `{` ` ` `int` `n = 10;` ` ` `Console.WriteLine(` ` ` `centeredIcosahedralNum(n));` ` ` ` ` `n = 12;` ` ` `Console.WriteLine(` ` ` `centeredIcosahedralNum(n));` ` ` `}` `}` `// This code is contributed by anuj_67.` |

## PHP

`<?php` `// PHP Program to find nth` `// Centered icosahedral number` `// Function to find` `// Centered icosahedral number` `function` `centeredIcosahedralNum(` `$n` `)` `{` ` ` `// Formula to calculate nth` ` ` `// Centered icosahedral number` ` ` `// and return it into main function.` ` ` `return` `(2 * ` `$n` `+ 1) * (5 *` ` ` `$n` `* ` `$n` `+ 5 * ` `$n` `+ 3) / 3;` `}` `// Driver Code` `$n` `= 10;` `echo` `centeredIcosahedralNum(` `$n` `),` `"\n"` `;` `$n` `= 12;` `echo` `centeredIcosahedralNum(` `$n` `),` `"\n"` `;` `// This code is contributed by m_kit` `?>` |

## Javascript

`<script>` `// Javascript Program to find nth` `// Centered icosahedral number` `// Function to find` `// Centered icosahedral number` `function` `centeredIcosahedralNum(n)` `{` ` ` `// Formula to calculate nth` ` ` `// Centered icosahedral number` ` ` `// and return it into main function.` ` ` `return` `parseInt((2 * n + 1) * (5 * n * n + 5 * n + 3) / 3);` `}` `// Driver Code` `let n = 10;` `document.write(centeredIcosahedralNum(n) + ` `"<br>"` `);` `n = 12;` `document.write(centeredIcosahedralNum(n));` `// This code is contributed by souravmahato348.` `</script>` |

**Output :**

3871 6525

Reference:

https://en.wikipedia.org/wiki/Centered_icosahedral_number

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