Question

I am reading an article on Fibonacci numbers at following link

http://xlinux.nist.gov/dads/HTML/kthOrderFibonacci.html

F(k)n = 0 for 0 ≤ n ≤ k-2

i am not getting what about above statement.

For example when k = 3 and n =2, 0 <= 2 < 1 which is not making sense? can any one please elaborate and pls give an example first 10 numbers 3rd order Fibonacci numbers

Answer 1

Basically you can’t sum the k values preceding n if n < k – 1, simply because there aren’t enough numbers. 🙂 as for your example, since n = k – 1 then f(n = 2) = 1.

n    f    reason
--------------------------------------------------
0    0    by definition (because n <= k - 2 = 1)
1    0    see above
2    1    by definition (because n = k - 1 = 2)
3    1    1 + 0 + 0
4    2    1 + 1 + 0
5    4    2 + 1 + 1
6    7    4 + 2 + 1
7    13   7 + 4 + 2
8    24   14+ 7 + 4