Program to check if N is a triacontagonal number

Given a number N, the task is to check if the number is a Triacontagonal number or not.
 

A Triacontagonal number is a 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 other 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 = 30 
Output: Yes 
Explanation: 
Second triacontagonal number is 30.
Input: 32 
Output: No 
 

 



Approach: 
 

  1. The Kth term of the triacontagonal number is given as: 
     

K^{th} Term =  \frac{28*K^{2} - 26*K}{2}

  1. As we have to check that the given number can be expressed as a triacontagonal number or not. This can be checked as follows: 
     

=> 

N =  \frac{28*K^{2} - 26*K}{2}

=> 

K = \frac{26 + \sqrt{224*N + 676}}{56}

 

  1.  
  2. Finally, check the value of computed using this formulae is an integer, which means that N is a triacontagonal number.

Below is the implementation of the above approach:
 

C++

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// C++ program to check whether a
// number is an triacontagonal
// number or not
#include <bits/stdc++.h>
using namespace std;
 
// Function to check whether a
// number is an triacontagonal
// number or not
bool istriacontagonal(int N)
{
    float n
        = (26 + sqrt(224 * N + 676))
          / 56;
 
    // Condition to check whether a
    // number is an triacontagonal
    // number or not
    return (n - (int)n) == 0;
}
 
// Driver Code
int main()
{
     
    // Given number
    int i = 30;
 
    // Function call
    if (istriacontagonal(i)) {
        cout << "Yes";
    }
    else {
        cout << "No";
    }
    return 0;
}

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Java

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// Java program to check whether a
// number is an triacontagonal
// number or not
class GFG{
 
// Function to check whether a
// number is an triacontagonal
// number or not
static boolean istriacontagonal(int N)
{
    float n = (float) ((26 + Math.sqrt(224 * N +
                                       676)) / 56);
     
    // Condition to check whether a
    // number is an triacontagonal
    // number or not
    return (n - (int)n) == 0;
}
 
// Driver code
public static void main(String[] args)
{
     
    // Given number
    int N = 30;
     
    // Function call
    if (istriacontagonal(N))
    {
        System.out.print("Yes");
    }
    else
    {
        System.out.print("No");
    }
}
}
 
// This code is contributed by shubham

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Python3

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# Python3 program to check whether a
# number is an triacontagonal
# number or not
import math;
 
# Function to check whether a
# number is an triacontagonal
# number or not
def istriacontagonal(N):
 
    n = (26 + math.sqrt(224 * N + 676)) // 56;
 
    # Condition to check whether a
    # number is an triacontagonal
    # number or not
    return (n - int(n)) == 0;
 
# Driver Code
 
# Given number
i = 30;
 
# Function call
if (istriacontagonal(i)):
    print("Yes");
else:
    print("No");
 
# This code is contributed by Code_Mech

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C#

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// C# program to check whether a
// number is an triacontagonal
// number or not
using System;
class GFG{
 
// Function to check whether a
// number is an triacontagonal
// number or not
static bool istriacontagonal(int N)
{
    float n = (float)((26 + Math.Sqrt(224 * N +
                                      676)) / 56);
     
    // Condition to check whether a
    // number is an triacontagonal
    // number or not
    return (n - (int)n) == 0;
}
 
// Driver code
public static void Main(String[] args)
{
     
    // Given number
    int N = 30;
     
    // Function call
    if (istriacontagonal(N))
    {
        Console.Write("Yes");
    }
    else
    {
        Console.Write("No");
    }
}
}
 
// This code is contributed by sapnasingh4991

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Output: 
Yes

 

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