Let $F_n$ denote the number of ways to mark (possibly zero) of $n$ flowers in a row such that no two marked flowers are adjacent. Pick a arbitrary flower on the circle and if you mark that flower then there are $F_{10}$ possibilities and if you don't then there are $F_{12}-1$. Note that $F_1=2$, $F_2=3$, $F_3=5$, $F_4=8$...If you mark the first of $n$ flowers then their are $F_{n-2}$ possibilities and if you don't there is $F_{n-1}$.