Problem
COM-B1-M10-P002 A \(2\times4\) Board
#2
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In how many ways can a \(2\times4\) board be tiled by dominoes?
Look at the last column.
Let \(a_n\) be the number of tilings of \(2\times n\). Then \(a_0=1\), \(a_1=1\), \(a_n=a_{n-1}+a_{n-2}\). Thus \(a_2=2\), \(a_3=3\), \(a_4=5\).
Classical Fibonacci tiling.