Question 9
A botanic garden has a line of 999 equally spaced positions, each containing at most one plant. In year 1 only the middle position has a plant. In year $n$, for every $n\ge2$, a position $X$ has a plant if and only if the total number of plants at $X$ and its two immediate neighbouring positions in the previous year is exactly one. Determine, with proof, the number of plants in year 128.