Check if a Number is Pentacontagon

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

Pentacontagon number is class of figurate number. It has 50 – sided polygon called pentacontagon. The N-th pentacontagon number count’s the 50 number of dots and all others dots are surrounding with a common sharing corner and make a pattern. The first few pentacontagonol numbers are 1, 50, 147, 292 ….

Examples:

Input: N = 50
Output: Yes
Explanation:
Second pentacontagon number is 50.

Input: 35
Output: No

Approach:
The K^th term of the pentacontagon number is given as K^{th} Term = (48*K^{2} – 46*K)/2
As we have to check that the given number can be expressed as a pentacontagon 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 pentacontagon number.

Below is the implementation of the above approach:

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

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

// Function to check whether the
// number is a pentacontagon number
bool is_pentacontagon(int N)
{
    float n = (66 + sqrt(384 * N + 2116)) / 96;

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

// Driver Code
int main()
{
    int i = 50;

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

    return 0;
}

Output:

Yes