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Program to check if N is a Hexadecagonal Number
• Last Updated : 23 Mar, 2021

Given an integer N, the task is to check if N is a Hexadecagonal Number or not. If the number N is an Hexadecagonal Number then print “Yes” else print “No”.

Hexadecagonal Number is class of figurate number and a perfect squares. It has 16-sided polygon called Hexadecagon or Hexakaidecagon. The nth Hexadecagonal Number counts the sixteen number of dots and all others dots are surrounding to its successive layer.The first few Hexadecagonal Numbers are 1, 16, 45, 88, 145, 216…

Examples:

Input: N = 16
Output: Yes
Explanation:
Second hexadecagonal number is 16.

Input: N = 30
Output: No

Approach:

1. The Kth term of the hexadecagonal number is given as

2. As we have to check that the given number can be expressed as a Hexadecagonal Number or not. This can be checked as:

=>
=>

3. If the value of K calculated using the above formula is an integer, then N is a Hexadecagonal Number.

4. Else N is not a Hexadecagonal Number.

Below is the implementation of the above approach:

## C++

 // C++ program for the above approach#include using namespace std; // Function to check if N is a// hexadecagonal numberbool ishexadecagonal(int N){    float n        = (12 + sqrt(112 * N + 144))          / 28;     // Condition to check if the    // number is a hexadecagonal number    return (n - (int)n) == 0;} // Driver Codeint main(){    // Given Number    int N = 16;     // Function call    if (ishexadecagonal(N)) {        cout << "Yes";    }    else {        cout << "No";    }    return 0;}

## Java

 // Java program for the above approachimport java.lang.Math; class GFG{     // Function to check if N is a// hexadecagonal numberpublic static boolean ishexadecagonal(int N){    double n = (12 + Math.sqrt(112 * N +                               144)) / 28;         // Condition to check if the    // number is a hexadecagonal number    return (n - (int)n) == 0;}     // Driver code   public static void main(String[] args){             // Given number    int N = 16;         // Function call    if (ishexadecagonal(N))    {        System.out.println("Yes");    }    else    {        System.out.println("No");    }}} // This code is contributed by divyeshrabadiya07

## Python3

 # Python3 program for the above approachfrom math import sqrt # Function to check if N is# a hexadecagonal numberdef ishexadecagonal(N):     n = (12 + sqrt(112 * N + 144)) / 28;     # Condition to check if the number    # is a hexadecagonal number    return (n - int(n)) == 0; # Driver codeif __name__ == "__main__":     # Given number    N = 16;     # Function call    if (ishexadecagonal(N)):        print("Yes");    else:        print("No");     # This code is contributed by AnkitRai01

## C#

 // C# program for the above approachusing System; class GFG{     // Function to check if N is a// hexadecagonal numberpublic static bool ishexadecagonal(int N){    double n = (12 + Math.Sqrt(112 * N +                             144)) / 28;         // Condition to check if the    // number is a hexadecagonal number    return (n - (int)n) == 0;}     // Driver codepublic static void Main(string[] args){             // Given number    int N = 16;         // Function call    if (ishexadecagonal(N))    {        Console.Write("Yes");    }    else    {        Console.Write("No");    }}} // This code is contributed by rutvik_56

## Javascript

 
Output:
Yes

Time Complexity: O(1)

Auxiliary Space: O(1)

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