type NumToArr<T extends number, Arr extends readonly unknown[]=[]> =
  T extends Arr['length']
  ? Arr
  : NumToArr<T,[...Arr, 0]>
type Pred<T extends number> =
  NumToArr<T> extends [infer Head, ...infer Rest] ? Rest["length"] : -1
// using recursion error suppression technique
// https://kgtkr.net/blog/2019/04/15/typescript-typelevelprogramming-error-suppression
type Sum<T extends number, U extends number> =
  NumToArr<T> extends infer TArr extends readonly unknown[]
  ? NumToArr<U> extends infer UArr extends readonly unknown[]
    ? [...TArr, ...UArr]["length"] : never : never
type Fibonacci<T extends number> =
  T extends 1 | 2
  ? 1
  : Fibonacci<Pred<Pred<T>>> extends infer N extends number
    ? Fibonacci<Pred<T>> extends infer M extends number
      ? Sum<N,M> : never : never

import type { Equal, Expect } from '@type-challenges/utils'

type cases = [
  Expect<Equal<Fibonacci<3>, 2>>,
  Expect<Equal<Fibonacci<8>, 21>>,
]