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):
    x = signature
    if n == 0:
        x = []
        return x
    if n == 1:
        x = [x[0]]
        return x
    if n == 2:
        for i in xrange(n - 3):
            x.append(x[-1])
        return x.append(x[-1] + x[-2])
    else:
        for i in xrange(n - 3):
            x.append(x[-1] + x[-2] + x[-3])
        return x


print tribonacci([1, 1, 1], 10)
print tribonacci([0, 0, 1], 10)
print tribonacci([0, 1, 1], 10)
print tribonacci([1, 0, 0], 10)
print tribonacci([0, 0, 0], 10)
print tribonacci([1, 2, 3], 10)
print tribonacci([3, 2, 1], 10)
print tribonacci([1, 1, 1], 1)
print tribonacci([300, 200, 100], 0)
print tribonacci([0.5, 0.5, 0.5], 30)
print tribonacci([0, 4, 4], 2)
print tribonacci([9, 11, 10], 2)