Triacontagon Number

Given a number N, the task is to find Nth Triacontagon number.

An Triacontagon number is class of figurate number. It has 30 – sided polygon called triacontagon. The N-th triacontagonal number count’s the 30 number of dots and all others dots are surrounding with a common sharing corner and make a pattern. The first few triacontagonol numbers are 1, 30, 87, 172 …

Examples:

Input: N = 2
Output: 30
Explanation:
The second triacontagonol number is 30.

Input: N = 3
Output: 87



Approach: The N-th triacontagonal 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 30 sided polygon is

    Tn =\frac{((30-2)n^2 - (30-4)n)}{2} =\frac{(28n^2 - 26n)}{2}

Below is the implementation of the above approach:

C++

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// C++ program for above approach
#include <bits/stdc++.h>
using namespace std;
  
// Finding the nth triacontagonal number
int triacontagonalNum(int n)
{
    return (28 * n * n - 26 * n) / 2;
}
  
// Driver code
int main()
{
    int n = 3;
      
    cout << "3rd triacontagonal Number is = " 
         << triacontagonalNum(n);
  
    return 0;
}
  
// This code is contributed by shivanisinghss2110

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C

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// C program for above approach
#include <stdio.h>
#include <stdlib.h>
  
// Finding the nth triacontagonal Number
int triacontagonalNum(int n)
{
    return (28 * n * n - 26 * n) / 2;
}
  
// Driver program to test above function
int main()
{
    int n = 3;
    printf("3rd triacontagonal Number is = %d",
           triacontagonalNum(n));
  
    return 0;
}

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Java

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// Java program for above approach
import java.io.*; 
import java.util.*; 
  
class GFG {
      
// Finding the nth triacontagonal number
static int triacontagonalNum(int n)
{
    return (28 * n * n - 26 * n) / 2;
}
  
// Driver code
public static void main(String[] args) 
    int n = 3;
      
    System.out.println("3rd triacontagonal Number is = "
                                    triacontagonalNum(n));
  
// This code is contributed by coder001

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Python3

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# Python3 program for above approach 
  
# Finding the nth triacontagonal Number 
def triacontagonalNum(n): 
  
    return (28 * n * n - 26 * n) // 2
  
# Driver Code
n = 3
print("3rd triacontagonal Number is = "
                   triacontagonalNum(n)) 
  
# This code is contributed by divyamohan123

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C#

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// C# program for above approach
using System;
  
class GFG{
      
// Finding the nth triacontagonal number
static int triacontagonalNum(int n)
{
    return (28 * n * n - 26 * n) / 2;
}
  
// Driver code
public static void Main() 
    int n = 3;
      
    Console.Write("3rd triacontagonal Number is = "
                               triacontagonalNum(n));
  
// This code is contributed by Akanksha_Rai

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Output:

3rd triacontagonal Number is = 87

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

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