tribonacci.fsx

(*
    Well met with Fibonacci bigger brother, AKA Tribonacci.
    As the name may already reveal, it works basically like a Fibonacci, but summing the last 3 (instead of 2) numbers of the sequence to generate the next. 
    And, worse part of it, regrettably I won't get to hear non-native Italian speakers trying to pronounce it :(
    So, if we are to start our Tribonacci sequence with [1,1,1] as a starting input (AKA signature), we have this sequence:
    [1,1,1,3,5,9,17,31,...]
    But what if we started with [0,0,1] as a signature? As starting with [0,1] instead of [1,1] basically shifts the common Fibonacci sequence 
    by once place, you may be tempted to think that we would get the same sequence shifted by 2 places, but that is not the case and we would get:
    [0,0,1,1,2,4,7,13,24,...]
    Well, you may have guessed it by now, but to be clear: you need to create a fibonacci function that given a signature array/list,
    returns the first n elements - signature included of the so seeded sequence.
    Signature will always contain 3 numbers; n will always be a non-negative number; if n==0, then return an empty array and be ready for anything else which is not clearly specified ;)

    taken from: https://www.codewars.com/kata/tribonacci-sequence/train/fsharp
*)

let trib signature n = 
    let _,_,t = match signature with
                |[x;y;z] ->
                    [ 1 .. n ]
                    |> Seq.fold(fun (a,b,c) idx -> (b, c, a+b+c)) (x,y,z)        
                |_ -> (0,0,0)
    t

let tribonacci signature n = 
    match n with
    | 0 -> []
    | 1 | 2 | 3 -> signature |> List.take n
    | _ ->  [ 1 .. n - 3]
            |> List.map(fun x -> trib signature x)
            |> List.append signature

let result = tribonacci [1;1;1] 10