A size n determinant has all 1s on the main diagonal and the first superdiagonal. It has all -1s on the first subdiagonal. It has zeros in all other places.

Show that this determinant evaluates to Fibonacci number F(n+1).

The determinant corresponding to n=5 is depicted below:

 | 1  1  0  0  0 |
 |-1  1  1  0  0 |
 | 0 -1  1  1  0 | = 8 = F(6)
 | 0  0 -1  1  1 |
 | 0  0  0 -1  1 |