Icosikaiheptagonal Number

Last Updated : 23 Jun, 2021

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

An icosikaiheptagonal number is a class of figurate numbers. It has 27 – sided polygon called icosikaiheptagon. The N-th icosikaiheptagonal number count’s the 27 number of dots and all other dots are surrounding with a common sharing corner and make a pattern. The first few icosikaiheptagonol numbers are 1, 27, 78, 154 …

Examples:

Input: N = 2
Output: 27
Explanation:
The second icosikaiheptagonol number is 27.
Input: N = 3
Output: 78

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

Nth term of s sided polygon = $\frac{((s-2)n^2 - (s-4)n)}{2}$
Therefore Nth term of 27 sided polygon is

$Tn =\frac{((27-2)n^2 - (27-4)n)}{2} =\frac{(25n^2 - 23n)}{2}$

Below is the implementation of the above approach:

C++

// C++ program to find N-th
// icosikaiheptagonal number
#include <bits/stdc++.h>
 
using namespace std;
// Function to find the nth
// icosikaiheptagonal Number
int icosikaiheptagonalNum(int n)
{
    return (25 * n * n - 23 * n) / 2;
}
 
// Driver code
int main()
{
    int n = 3;
 
    cout << "3rd icosikaiheptagonal Number is "
         << icosikaiheptagonalNum(n);
 
    return 0;
}

Java

// Java program to find N-th 
// icosikaiheptagonal number 
class GFG{ 
 
// Function to find the nth 
// icosikaiheptagonal number 
static int icosikaiheptagonalNum(int n) 
{ 
    return (25 * n * n - 23 * n) / 2; 
} 
 
// Driver code 
public static void main(String[] args) 
{ 
    int n = 3; 
    System.out.print("3rd icosikaiheptagonal Number is " + 
                                icosikaiheptagonalNum(n)); 
} 
} 
 
// This code is contributed by shubham

Python3

# Python3 program to find N-th
# icosikaiheptagonal number
 
# Function to find the nth
# icosikaiheptagonal Number
def icosikaiheptagonalNum(n):
 
    return (25 * n * n - 23 * n) // 2;
 
# Driver code
n = 3;
print("3rd icosikaiheptagonal Number is ", 
                icosikaiheptagonalNum(n));
 
# This code is contributed by Code_Mech

C#

// C# program to find N-th 
// icosikaiheptagonal number 
using System;
 
class GFG{ 
 
// Function to find the nth 
// icosikaiheptagonal number 
static int icosikaiheptagonal(int n) 
{ 
    return (25 * n * n - 23 * n) / 2; 
} 
 
// Driver code 
public static void Main(String[] args)
{
    int n = 3; 
     
    Console.Write("3rd icosikaiheptagonal Number is " + 
                                icosikaiheptagonal(n)); 
} 
} 
 
// This code is contributed by shivanisinghss2110

Javascript

<script>
 
// javascript program to find N-th
// icosikaiheptagonal number
 
// Function to find the nth
// icosikaiheptagonal Number
function icosikaiheptagonalNum( n)
{
    return (25 * n * n - 23 * n) / 2;
}
 
// Driver code
let n = 3;
    document.write("3rd icosikaiheptagonal Number is "+ icosikaiheptagonalNum(n));
 
// This code is contributed by todaysgaurav 
 
</script>