Answer:
f(n) = f(n+2) - f(n+1)
sequence: ...,−8,5,−3,2,−1,1,0,1,1,2,3,5,8,...
Explanation:
Normal Fibonacci: f(n) = f(n-2) + f(n-1), sequence 0 1 1 2 3 5 8 ...
Now, replace n by n+2:
f(n+2) = f(n) + f(n+1)
and bring f(n) to the left while moving f(n+2) to the right:
f(n) = f(n+2) - f(n+1)
Now we can start applying it backwards.
f(0) = f(2) - f(1) = 0
f(-1) = f(1) - f(0) = 1
f(-2) = f(0) - f(-1) = -1
f(-3) = f(-1) - f(-2) = 2
etc...
