yeah actually you needed to define only the first 2 terms of sequence rather than all the sequence. However, I liked how you used memoization

Alr, could've probably guessed that but being more sure is always nice. Thx :D

One-time math calculations are normally O(1), although it depends on how they are implemented.

When I first saw this, I was like what??!! :D

Probably a 6

What kata rank would you give this one (for Python)?

face => palm

It's not cheating. It's Python.

What an ingenious way!!!

Yes, it's O(n^2): you're using a single loop over O(n^2) instead of two nested loops over O(n) both with common complexity of O(n^2). Also, probably it's not so effective because it's using additional checks instead of just using built-in loops (but this should be benchmarked, not speculated), and it's much less readable; but it has the same time complexity.

a*(a+1) = n*n

Ok, if you say so, what is the time complexity of my own code since maybe i don't really know about time complexity

The task is to generate O(n^2) elements. You can't do O(n^2) work in less then O(n^2) steps.

Bad practice O(n^2)

Because originally it is a Ruby kata, and it's pretty much using a built-in. The kata's rank is shared amongst all languages.