010 - Tribonacci Sequence.py

"""
Tribonacci works basically like a Fibonacci, but summing the last 3 (instead of 2) numbers of the sequence to generate the next. 

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, ...]

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 ;)
"""


def tribonacci(signature, n):
    if n >= 3:
        for i in range(3, n):
            signature.append(signature[i-3] + signature[i-2] + signature[i-1]) # signature.append(sum(signature[-3:])) seems to be slower

    return signature[:n]