f(h) = 1 + f(h-1) + f(h-2)
Since f(h-1) >= f(h-2), we get
f(h) > 2f(h-2) (for all h >= 1)
| f(7) > 2f(5) | f(8) > 2f(6) |
| f(7) > 22f(3) | f(8) > 22f(4) |
| f(7) > 23f(1) | f(8) > 23f(2) |
| f(7) > 232 | f(8) > 24f(0) |
| f(7) > 24 | f(8) > 24 |
In general,
f(h) > 2ceiling(h/2) > 2h/2
where ceiling(x) means the smallest integer that is >= x.