Check counts in a nonadjacent binary-schedule investigation

A binary schedule has 9 labelled slots, numbered from 1 to 9. A 1 means active and a 0 means inactive. Different bit strings are different schedules. No adjacent slots may both contain 1

This is a line: the first and last slots are not adjacent. Let zₙ and oₙ count valid schedules ending in 0 and 1, respectively. Start with z₁=o₁=1, and use zₙ₊₁=zₙ+oₙ, oₙ₊₁=zₙ