Implementing the Fibonacci sequence for the last n elements: The nBonacci sequence

I was curious about how I can implement the Fibonacci sequence for summing the last n elements instead of just the last 2. So I was thinking about implementing a function nBonacci(n,m) where n is the number of last elements we gotta sum, and m is the number of elements in this list.

The Fibonacci sequence starts with 2 ones, and each following element is the sum of the 2 previous numbers.

Let’s make a generalization: The nBonacci sequence starts with n ones, and each following element is the sum of the previous n numbers.

I want to define the nBonacci function that takes the positive integer n and a positive integer m, with m>n, and returns a list with the first m elements of the nBonacci sequence corresponding to the value n.

For example, nBonacci(3,8) should return the list [1, 1, 1, 3, 5, 9, 17, 31].

def fib(num):
    a = 0
    b = 1
    while b <= num:
        prev_a = a
        a = b
        b = prev_a +b

The problem is that I don’t know the number of times I gotta sum. Does anyone have an idea and a suggestion of resolution?

>Solution :

The nBonacci sequence will always have to start with n ones, or the sequence could never start. Therefore, we can just take advantage of the range() function and slice the existing list:

def nfib(n, m):
    lst = [1] * n
    for i in range(n, m):
        lst.append(sum(lst[i-n:i]))
    return lst


print(nfib(3, 8))  # => [1, 1, 1, 3, 5, 9, 17, 31]