Anti-fibonacci Number

The anti-Fibonacci numbers compose a closely sequence related to the Fibonacci sequence. It satisfies the following recursion formula:
f(k+2) = f(k) - f(k+1)\,
Usually, it is made to start with 1, 0. Then, it goes like this:
1,0,1,-1,2,-3,5,-8, \dots\,
For easy comparison: The Fibonacci sequence satisfies
f(k+2) = f(k) + f(k+1)\,
and goes like this:
0,1,1,2,3,5,8, \dots\,
   
If the Fibonacci sequence is extended backwards -
\dots -8,5,-3,2,-1,1,0,1,1,2,3,5,8, \dots\,
- the anti-Fibonaccis also appear.

 

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