Fibonacci Sequence

In this medium-level challenge, you'll implement a generic Fibonacci<T> that takes a number T and returns its corresponding Fibonacci number. The sequence starts 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on.

type Result1 = Fibonacci<3> // 2
type Result2 = Fibonacci<8> // 21

Detailed Explanation

Since TypeScript's type system doesn't support arithmetic, we simulate addition and counting using tuple lengths. We track the current position, the previous two Fibonacci values (as tuples whose lengths represent the numbers), and recurse until we reach position T.

type Fibonacci<
  T extends number,
  CurrentIndex extends readonly number[] = [1],
  Prev extends readonly number[] = [],
  Current extends readonly number[] = [1]
> = CurrentIndex['length'] extends T
  ? Current['length']
  : Fibonacci<T, [...CurrentIndex, 1], Current, [...Prev, ...Current]>

How it works:

• CurrentIndex is a tuple that grows by one element each step, tracking our position in the sequence
• Prev holds a tuple whose length is the (n-1)th Fibonacci number
• Current holds a tuple whose length is the nth Fibonacci number
• When CurrentIndex['length'] equals T, we return Current['length'] as the result
• Otherwise, we recurse: the new Prev becomes Current, and the new Current becomes [...Prev, ...Current], which simulates addition via tuple concatenation

This challenge helps you understand recursive type computation using tuple length arithmetic and how to apply this concept in real-world scenarios.