HI everyone,

What means k,
what should i make in this Kata

Is it too much to ask why 0 => 7 and 1 => 4 ? Sry but the description is too ambiguous for me.

Could someone please explain how shall one consider the test cases where h == 1 and a > 0?

( JS, probably others )

Fixed tests with only red balls and only black balls would be good, to catch solutions that somehow fail on those edge cases.

i don't understand the task and "Euler transform"

There are lots of Fibonacci-type katas with an O(log n) performance requirement. Here's one that similarly allows for arbitrary coefficients, but also allows for more lags: https://www.codewars.com/kata/5d7bb3eda58b36000fcc0bbb

Use of double for his kind of task is arguable (but not exactly wrong). All values in domain of this problem are rational numbers, so it is possible to calculate the answer precisely. It could be worth to consider if an approximate answer is indeed preferred to precise one.

If you decide to stick to floating point numbers, I would advise double checking that they are handled correctly. Rounding a double to n decimal places and strict equality comparison is almost always wrong and susceptible to rounding issues. It's highly probable that such checks won't work well, and some valid solutions will be rejected (some very basic explanation here).