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Program for Centered Icosahedral Number
• Difficulty Level : Basic
• Last Updated : 07 Apr, 2021

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 numberint 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 Codeint 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 Coden = 10print(centeredIcosahedralNum(n)) n = 12print(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

 

## Javascript

 
Output :
3871
6525

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