Fibonacci, Tribonacci and friends.py

# If you have completed the Tribonacci sequence kata, you would know by now that mister Fibonacci has at least a bigger brother. If not, give it a quick look to get how things work.

# Well, time to expand the family a little more: think of a Quadribonacci starting with a signature of 4 elements and each following element is the sum of the 4 previous, a Pentabonacci (well Cinquebonacci would probably sound a bit more italian, but it would also sound really awful) with a signature of 5 elements and each following element is the sum of the 5 previous, and so on.

# Well, guess what? You have to build a Xbonacci function that takes a signature of X elements - and remember each next element is the sum of the last X elements - and returns the first n elements of the so seeded sequence.

# xbonacci {1,1,1,1} 10 = {1,1,1,1,4,7,13,25,49,94}
# xbonacci {0,0,0,0,1} 10 = {0,0,0,0,1,1,2,4,8,16}
# xbonacci {1,0,0,0,0,0,1} 10 = {1,0,0,0,0,0,1,2,3,6}
# xbonacci {1,1} produces the Fibonacci sequence

def xbonacci(signature, n):
    ans = signature[:]
    
    for i in range(len(signature), n):
        ans.append(sum(ans[i-len(signature):i]))
    
    return ans[:n]