Problem
COM-B1-M11-P017 A \(2\times7\) Board
#17
★★★☆☆ Level 3 of 5
In how many ways can a \(2\times7\) board be tiled by dominoes?
The last column is vertical or the last two columns use two horizontal dominoes.
Let \(a_n\) be the number of tilings. Then \(a_n=a_{n-1}+a_{n-2}\), \(a_0=1\), \(a_1=1\). We get \(a_7=21\).
A recurrence may appear late in a mixed sheet.