Recursive bullet style on nested ordered lists

Question

I'd like to have ordered lists automatically styled based on its level as such:

1. Item
  a. Item
    i. Item
      1. Item
        a. Item
          i. Item
           ...

As you can see it is repeating this sequence: number > letter > roman numeral

I can do this through CSS as

ol {
    list-style-type:decimal;
}
ol > li > ol {
    list-style-type:lower-alpha;
}
ol > li > ol > li > ol {
    list-style-type:lower-roman;
}
ol > li > ol > li > ol > li > ol {
    list-style-type:decimal;
}
...

but this is tedious and I don't know how many levels I would need.

Is there a cleaner way of doing this through CSS?

I should note that I am doing this to style up an HTML editor and the generated HTML has this very basic structure:

<ol>
  <li>
    <ol>
      <li>
        ..

I have no control of the HTML and I can't add classes to it or anything.

Answer 1

It's not the prettiest solution, but we've decided to go with this one for now:
_{Thanks to @Vucko for suggesting that we didn't need the direct child selectors}

ol,
ol ol ol ol,
ol ol ol ol ol ol ol {
    list-style-type:decimal;
}
ol ol,
ol ol ol ol ol,
ol ol ol ol ol ol ol ol {
    list-style-type:lower-alpha;
}
ol ol ol,
ol ol ol ol ol ol,
ol ol ol ol ol ol ol ol ol {
    list-style-type:lower-roman;
}

This obviously works only up until the 9th level, but we don't think any list will go down this deep for our scenario.

_{If only there was some sort of :nth-level() selector...}