Recurssion and iteration don't scale well. Factorial calculation with big numbers is a problem. The idea for this kata is to find a method that reduces the number of iterations/recursive calls to the minimum necessary to find a solution. You need a little bit of math before implementing a solution.

There are other solutions without using a recursive implementation.

Yes, I would like it if you do.

I've updated the tests and added some comments here and there. Hope it helps.

Please, let me know if you find anything else.

This is actually the same as this:

function tetrahedron(n) {
  n * (n + 1) * (3 * Math.ceil(n / 3) + (n - 1) % 3) / 6;
}

I should have seen this, and also that 3 * Math.ceil(n / 3) + (n - 1) % 3 is the same as n + 2

I had replied before, but it looks like my reply was not posted.
Anyway. Thanks for your comments. I have improved this kata a little bit. I now use 797651 in my tests.
Let me know if you have any other improvement.

What should I return when input is null or empty string?