Pentacontagon number

Given a number N, the task is to find N^th Pentacontagon number. 

A Pentacontagon number is class of figurate number. It has 50 – sided polygon called pentacontagon. The N-th pentacontagon number count’s the 50 number of dots and all others dots are surrounding with a common sharing corner and make a pattern. The first few pentacontagonol numbers are 1, 50, 147, 292 …

Examples:

Input: N = 2 
Output: 50 
Explanation:
The second pentacontagonol number is 50. 
Input: N = 3 
Output: 147 

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

• Nth term of s sided polygon = 
  
• Therefore Nth term of 50 sided polygon is
  

Below is the implementation of the above approach: 

C++

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

// Finding the nth pentacontagon Number
int pentacontagonNum(int n)
{
    return (48 * n * n - 46 * n) / 2;
}

// Driver Code
int main()
{
    int n = 3;
    cout << "3rd pentacontagon Number is = "
         << pentacontagonNum(n);

    return 0;
}

// This code is contributed by Akanksha_Rai

C

// C program for above approach
#include <stdio.h>
#include <stdlib.h>

// Finding the nth pentacontagon Number
int pentacontagonNum(int n)
{
    return (48 * n * n - 46 * n) / 2;
}

// Driver program to test above function
int main()
{
    int n = 3;
    printf("3rd pentacontagon Number is = %d",
           pentacontagonNum(n));

    return 0;
}

Java

// Java program for above approach
import java.util.*;

class GFG {

// Finding the nth pentacontagon number
static int pentacontagonNum(int n)
{
    return (48 * n * n - 46 * n) / 2;
}

// Driver code
public static void main(String[] args)
{
    int n = 3;

    System.out.println("3rd pentacontagon Number is = " +
                                    pentacontagonNum(n));
}
}

// This code is contributed by offbeat

Python3

# Python3 program for above approach

# Finding the nth pentacontagon Number
def pentacontagonNum(n):

    return (48 * n * n - 46 * n) // 2

# Driver Code
n = 3
print("3rd pentacontagon Number is = ",
                   pentacontagonNum(n))

# This code is contributed by divyamohan123

C#

// C# program for above approach
using System;

class GFG {

// Finding the nth pentacontagon number
static int pentacontagonNum(int n)
{
    return (48 * n * n - 46 * n) / 2;
}

// Driver code
public static void Main(string[] args)
{
    int n = 3;

    Console.Write("3rd pentacontagon Number is = " +
                               pentacontagonNum(n));
}
}

// This code is contributed by rutvik_56

Javascript

<script>

// javascript program for above approach

// Finding the nth pentacontagon Number
function pentacontagonNum( n)
{
    return (48 * n * n - 46 * n) / 2;
}

// Driver code
let n = 3;
document.write("3rd pentacontagon Number is " + pentacontagonNum(n));

// This code contributed by gauravrajput1

</script>

Output:

3rd pentacontagon Number is = 147

Time Complexity: O(1)

Auxiliary Space: O(1)

Reference: https://en.wikipedia.org/wiki/Pentacontagon