Check if a Number is Hexacontagon

Given an integer N, the task is to check if it is a hexacontagon number or not.

Hexacontagon number is class of figurate number. It has 60 – sided polygon called hexacontagon. The N-th hexacontagon number count’s the 60 number of dots and all others dots are surrounding with a common sharing corner and make a pattern. The first few hexacontagonol numbers are 1, 60, 177, 352 …..

Examples:

Input: N = 60
Output: Yes
Explanation:
Second hexacontagon number is 60.

Input: 35
Output: No

Approach:

The K^th term of the hexacontagon number is given as K^th Term = (58*K^{2} – 56*K)/2
As we have to check that the given number can be expressed as a hexacontagon number or not. This can be checked as follows –

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

Below is the implementation of the above approach:

// C++ implementation to check whether
// a number is a hexacontagon number or not

#include <bits/stdc++.h>
using namespace std;

// Function to check whether the
// number is a hexacontagon number
bool is_hexacontagon(int N)
{
    float n = (56 + sqrt(464 * N + 3136)) / 116;

    // Condition to check if the
    // number is a hexacontagon number
    return (n - (int)n) == 0;
}

// Driver Code
int main()
{
    int i = 60;

    // Function call
    if (is_hexacontagon(i)) {
        cout << "Yes";
    } else {
        cout << "No";
    }

    return 0;
}

Output:

Yes