Find the Nth Triacontakaihenagonal Number

Given a number N, the task is to find N^th triacontakaihenagonal number.

A triacontakaihenagonal number is class of figurate number. It has 31 – sided polygon called triacontakaihenagon. The N-th triacontakaihenagonal number count’s the 31 number of dots and all others dots are surrounding with a common sharing corner and make a pattern. The first few triacontakaihenagonol numbers are 1, 31, 90, 178 …

Examples:

Input: N = 2
Output: 31
Explanation:
The second triacontakaihenagonol number is 31.

Input: N = 3
Output: 90

Approach: The N-th triacontakaihenagonal number is given by the formula:
Nth term of s sided polygon = (((s-2)n^2 – (s-4)n)) / 2

Therefore Nth term of 31 sided polygon is –

Below is the implementation of the above approach:

// C program for the above approach
#include <stdio.h>
#include <stdlib.h>

// Finding the nth triacontakaihenagonal Number
int triacontakaihenagonalNum(int n)
{
    return (29 * n * n - 27 * n) / 2; 
}

// Driver program to test the above function
int main()
{
    int n = 3;
    printf("3rd triacontakaihenagonal Number is = %d", 
           triacontakaihenagonalNum(n));

    return 0;
}

Output:

3rd triacontakaihenagonal Number is =  90