# Program for Centered Icosahedral Number

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  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

 

Output :

3871
6525


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Improved By : jit_t, vt_m