Fibonacci Sequence in TypeScript type

gistfile1.txt

// 1st attempt
type Arr<
	T extends number,
	Carry extends number[] = []
> = Carry['length'] extends T ? Carry : Arr<T, [0, ...Carry]>
type Add<A extends number, B extends number> = [...Arr<A>, ...Arr<B>]['length']
type Subtract<A extends number, B extends number> =
	Arr<A> extends [...Arr<B>, ...infer R] ? R['length'] : 0

type Compute<
	Target extends number,
	Sequence extends number[] = [0, 1]
> = Sequence['length'] extends Target
	? Sequence extends [...infer R, infer Last]
		? Last
		: never
	: Compute<
			Target,
			// @ts-ignore
			[
				...Sequence,
				Add<
					Sequence[Subtract<Sequence['length'], 1>],
					Sequence[Subtract<Sequence['length'], 2>]
				>
			]
		>

type Fibonacci<Target extends number> = Target extends 0
	? 0
	: Target extends 1
		? 1
		: // @ts-ignore
			Compute<Add<Target, 1>>


type A = Fibonacci<17>

// 2nd attempt
type Compute<
	Limit extends number,
	Sequence extends number[][] = [[0], [0]]
> = Sequence['length'] extends Limit
	? Sequence extends [...any, infer Last extends any[]]
		? Last['length']
		: 0
	: Sequence extends [...any, infer A extends any[], infer B extends any[]]
		? Compute<Limit, [...Sequence, [...A, ...B]]>
		: never

type Fibonacci<Target extends number> = Target extends 0
	? 0
	: Target extends 1
		? 1
		: Compute<Target>


type A = Fibonacci<20>