11. Arrange 10 flowers in a row using red, yellow, and blue flowers (assuming there are plenty of each color), and yellow flowers cannot be adjacent. How many different arrangements are there (the 10 flowers can be of one color or two colors)?
11. Let $x_{n}$ be the number of different arrangements of $n$ flowers that meet the requirements. Then
$$
x_{1}=3, x_{2}=3^{2}-1=8 \text {. }
$$

When $n \geqslant 3$, let the arrangement of $n$ flowers be $a_{1}, a_{2}, \cdots, a_{n}$. If $a_{1}$ is a red or blue flower, then $a_{2}, a_{3}, \cdots, a_{n}$ is an arrangement of $n-1$ flowers that meets the conditions; if $a_{1}$ is a yellow flower, then $a_{2}$ must be a red or blue flower, in which case $a_{3}, a_{4}, \cdots, a_{n}$ is an arrangement of $n-2$ flowers that meets the conditions.
$$
\begin{array}{l}
\text { Thus, } x_{n}=2 x_{n-1}+2 x_{n-2} . \\
\text { Hence } x_{3}=2 x_{2}+2 x_{1}=22, \\
x_{4}=2 x_{3}+2 x_{2}=60, \\
x_{5}=2 x_{4}+2 x_{3}=164, \\
x_{6}=2 x_{5}+2 x_{4}=448, \\
x_{7}=2 x_{6}+2 x_{5}=1224, \\
x_{8}=2 x_{7}+2 x_{6}=3344, \\
x_{9}=2 x_{8}+2 x_{7}=9136, \\
x_{10}=2 x_{9}+2 x_{8}=24960 .
\end{array}
$$

【Note】The general term of $\left\{x_{n}\right\}$ in this problem is
$$
x_{n}=\frac{9+5 \sqrt{3}}{6}(1+\sqrt{3})^{n-1}+\frac{9-5 \sqrt{3}}{6}(1-\sqrt{3})^{n-1} .
$$