120-gon number

Given a number N, the task is to find N^th 120-gon number.

A 120-gon number is a class of figurate numbers. It has 120 – sided polygon called 120-gon. The N-th 120-gon number count’s the 120 number of dots and all other dots are surrounding with a common sharing corner and make a pattern. The first few 120-gon numbers are 1, 120, 357, 712, 1185, 1776, …

Examples:

Input: N = 2 
Output: 120 
Explanation:
The second 120-gonol number is 120. 
Input: N = 3 
Output: 357 

Approach: The N-th 120-gon number is given by the formula:

• Nth term of s sided polygon = 
  
• Therefore Nth term of 120 sided polygon is
  

• 
  

Below is the implementation of the above approach:

C++

// C++ implementation for above approach
#include <bits/stdc++.h>
using namespace std;

// Function to find the
// nth 120-gon Number
int gonNum120(int n)
{
    return (118 * n * n - 116 * n) / 2;
}

// Driver Code
int main()
{
    int n = 3;
    cout << gonNum120(n);

    return 0;
}

Java

// Java program for above approach
class GFG{

// Function to find the
// nth 120-gon Number
static int gonNum120(int n)
{
    return (118 * n * n - 116 * n) / 2;
}

// Driver code
public static void main(String[] args)
{
    int n = 3;
    System.out.print(gonNum120(n));
}
}

// This code is contributed by shubham

Python3

# Python3 implementation for above approach

# Function to find the
# nth 120-gon Number
def gonNum120(n):

    return (118 * n * n - 116 * n) // 2;

# Driver Code
n = 3;
print(gonNum120(n));

# This code is contributed by Code_Mech

C#

// C# program for above approach
using System;
class GFG{

// Function to find the
// nth 120-gon Number
static int gonNum120(int n)
{
    return (118 * n * n - 116 * n) / 2;
}

// Driver code
public static void Main(String[] args)
{
    int n = 3;
    Console.Write(gonNum120(n));
}
}

// This code is contributed by sapnasingh4991

Javascript

<script>

// JavaScript implementation for above approach

// Function to find the
// nth 120-gon Number
function gonNum120(n)
{
    return (118 * n * n - 116 * n) / 2;
}

// Driver Code
var n = 3;
document.write(gonNum120(n));


</script>

Output:

357

Time Complexity: O(1)

Reference: https://en.wikipedia.org/wiki/120-gon