Program to find Star number

A number is termed as star number, if it is a centered figurate number that represents a centered hexagram (six-pointed star) similar to chinese checker game. The few star numbers are 1, 13, 37, 73, 121, 181, 253, 337, 433, ….
Examples:

Input : n = 2
Output : 13

Input : n = 4
Output : 73

Input : n = 6
Output : 181

If we take few examples, we can notice that the n-th star number is given by the formula: 

n-th star number = 6n(n - 1) + 1 

Below is the implementation of above formula.

C++

// C++ program to find star number
#include <bits/stdc++.h>
using namespace std;

// Returns n-th star number
int findStarNum(int n)
{
    return (6 * n * (n - 1) + 1);
}

// Driver code
int main()
{
    int n = 3;
    cout << findStarNum(n);
    return 0;
}

Java

// Java program to find star number
import java.io.*;

class GFG {
    // Returns n-th star number
    static int findStarNum(int n)
    {
        return (6 * n * (n - 1) + 1);
    }

    // Driver code
    public static void main(String args[])
    {
        int n = 3;
        System.out.println(findStarNum(n));
    }
}

// This code is contributed
// by Nikita Tiwari.

Python3

# Python3 program to
# find star number

# Returns n-th
# star number
def findStarNum(n):

    return (6 * n * (n - 1) + 1)

# Driver code
n = 3
print(findStarNum(n))

# This code is contributed by Smitha Dinesh Semwal

C#

// C# program to find star number
using System;

class GFG {
    // Returns n-th star number
    static int findStarNum(int n)
    {
        return (6 * n * (n - 1) + 1);
    }

    // Driver code
    public static void Main()
    {
        int n = 3;
        Console.Write(findStarNum(n));
    }
}

// This code is contributed
// by vt_m.

PHP

<?php
//PHP program to find star number

// Returns n-th star number
function findStarNum($n)
{
    return (6 * $n * ($n - 1) + 1);
}

// Driver code
$n = 3;
echo findStarNum($n);

// This code is contributed by ajit
?>

Javascript

<script>
// Javascript program to find star number

// Returns n-th star number
function findStarNum(n)
{
    return (6 * n * (n - 1) + 1);
}

// Driver code
let n = 3;
document.write(findStarNum(n));

// This code is contributed by rishavmahato348.
</script>

Output :

37

Time complexity: O(1) since performing constant operations

Space complexity: O(1) since using constant variables

Interesting Properties of Start Numbers: 

1. The digital root of a star number is always 1 or 4, and progresses in the sequence 1, 4, 1.
2. The last two digits of a star number in base 10 are always 01, 13, 21, 33, 37, 41, 53, 61, 73, 81, or 93.
3. The generating function for the star numbers is 
   

x*(x^2 + 10*x + 1) / (1-x)^3 = x + 13*x^2 + 37*x^3 +73*x^4 .......

1. The star numbers satisfy the linear recurrence equation 
   

S(n) = S(n-1) + 12(n-1)

References :
http://mathworld.wolfram.com/StarNumber.html
https://en.wikipedia.org/wiki/Star_number
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