tribonacci_sequence.py

#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 ;)

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

#[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 :)]

def tribonacci(signature, n):
	tribo = []
	if n > 0 and n < 3:
		for i in range(n):
			tribo.append(signature[i])
	elif n >= 3:
		tribo = signature
	
	for i in range(n-3):
		sum = tribo[i] + tribo[i+1] + tribo[i+2]
		tribo.append(sum)
	
	return tribo