Triacontakaihenagonal Number

A triacontakaihenagonal number is a type of figurate number that represents a polygon with 31 sides. It is given by the formula:

T(31,n) = 31n^2 - 31n + 1

where n is the nth triacontakaihenagonal number.

Implementation

To calculate the triacontakaihenagonal number, we can write a simple function in Python:

def triacontakaihenagonal(n):
    return 31 * n**2 - 31 * n + 1

This function takes an integer n as input and returns the nth triacontakaihenagonal number.

Example

Let's test our function with some examples:

>>> triacontakaihenagonal(1)
1
>>> triacontakaihenagonal(2)
61
>>> triacontakaihenagonal(3)
181

Applications

Triacontakaihenagonal numbers have applications in geometry, number theory, and combinatorics. They represent the number of points that can be arranged in a triangular grid with 31 points on each side.

They also have connections to the theory of modular forms, which are important in fields such as algebraic geometry and number theory.

Overall, triacontakaihenagonal numbers are an interesting and important concept in mathematics.