Icosikaiheptagonal Number

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++

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// 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;
}

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Java

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// 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

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Python3

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# 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

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C#

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// 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

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Output:

3rd icosikaiheptagonal Number is 78

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

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