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Icosikaiheptagonal Number

  • Last Updated : 23 Jun, 2021

Given a number N, the task is to find Nth 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>
Output: 
3rd icosikaiheptagonal Number is 78

 

Time Complexity: O(1)

Auxiliary Space: O(1)

Reference: http://www.2dcurves.com/line/linep.html

 

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