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

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

3. Finally, check the value computed using this formula is an integer, which means that N is a triacontagonal number.

Below is the implementation of the above approach:

## C++

 // C++ program to check whether a// number is an triacontagonal// number or not#include using namespace std; // Function to check whether a// number is an triacontagonal// number or notbool 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 Codeint main(){         // Given number    int i = 30;     // Function call    if (istriacontagonal(i)) {        cout << "Yes";    }    else {        cout << "No";    }    return 0;}

## Java

 // Java program to check whether a// number is an triacontagonal// number or notclass GFG{ // Function to check whether a// number is an triacontagonal// number or notstatic 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 codepublic 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

## Python3

 # Python3 program to check whether a# number is an triacontagonal# number or notimport math; # Function to check whether a# number is an triacontagonal# number or notdef 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 numberi = 30; # Function callif (istriacontagonal(i)):    print("Yes");else:    print("No"); # This code is contributed by Code_Mech

## C#

 // C# program to check whether a// number is an triacontagonal// number or notusing System;class GFG{ // Function to check whether a// number is an triacontagonal// number or notstatic 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 codepublic 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

## Javascript

 

Output

Yes

Time Complexity: O(log(n)), since sqrt() function has been used
Auxiliary Space: O(1)

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