Tribonacci Sequence - CodeWars

index.pug

p Well met with Fibonacci bigger brother, AKA Tribonacci.

p 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 :(

p So, if we are to start our Tribonacci sequence with [1, 1, 1] as a starting input (AKA signature), we have this sequence:

code [1, 1 ,1, 3, 5, 9, 17, 31, ...]
p 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:

code [0, 0, 1, 1, 2, 4, 7, 13, 24, ...]
p 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.

p 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 ;)

p If you enjoyed this kata more advanced and generalized version of it can be found in the Xbonacci kata

p [Personal thanks to Professor Jim Fowler on Coursera for his awesome classes that I really recommend to any math enthusiast and for showing me this mathematical curiosity too with his usual contagious passion :)]

script.babel

function tribonacci(signature, n){
  if (n < 3) return signature.slice(0, n)
  if (n === 3) return signature
  const [x, y, z] = signature.slice(-3)
  return tribonacci(signature.concat(x + y + z), n - 1)
}

tribonacci-sequence-codewars.markdown

Tribonacci Sequence - CodeWars

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