Given a 2 2 tile and seven dominoes ( 2 1 tile), find the number of ways of tiling (that is, cover without leaving gaps and without overlapping of any two tiles) a 2 7 rectangle using some of these tiles.

Question

Quantrex Academy · Accepted Answer

Correct answer: 85

aligned & a_n=2 a_ n-2 +a_ n-1 & a₁=1, a₂=3 & a₃=2 a₁+a₂=2(1)+3=5 & a₄=2 a₂+a₃=2(3)+5=11 & a₅=2 a₃+a₄=2(5)+11=21 & a₆=2(11)+21=43 & a₇=2(21)+43=42+43=85 aligned

Given a 2 2 tile and seven dominoes ( 2 1 tile), find the number of ways of tiling (that is, cover without leaving gaps and without overlapping of any two tiles) a 2 7 rectangle using some of these tiles.

Correct answer

Step-by-step solution

More from Permutation and Combination