tribonacci-sequence.js

// 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 (except in C return NULL) and be ready for anything else which is not clearly specified ;)

function tribonacci(signature,n){
  if (n <= 3) return signature.slice(0, n);
  let number;
  for (let i = 3; i < n; i++){
    number = signature[i-1] + signature[i-2] + signature[i-3];
    signature.push(number);
  }
  return signature;
}