1 .
Let $n \geq 1$ be an integer and consider a $2 \times n$ board $B_n$ consisting of a total of $2n$ square cells.
The top part of the figure below shows $B_{13}$.
A brick is a horizontal or vertical board consisting of 2 square cells; see the bottom part of the figure
above. A tiling of the board $B_n$ is a placement of bricks on the board such that
Let $T_n$ be the number of different tilings of the board $B_n$. Which of the following is true for any $n \geq 3$?
A brick is a horizontal or vertical board consisting of 2 square cells; see the bottom part of the figure
above. A tiling of the board $B_n$ is a placement of bricks on the board such that
- the bricks exactly cover $B_n$ and
- no two bricks overlap.
Let $T_n$ be the number of different tilings of the board $B_n$. Which of the following is true for any $n \geq 3$?
(a)
$T_n = 2 \cdot T_{n - 1} + T_{n - 2}$
(b)
$T_n = T_{n + 1} + T_{n + 2}$
(c)
$T_n = T_{n - 1} + 2 \cdot T_{n - 2}$
(d)
$T_n = T_{n - 1} + T_{n - 2}$