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Problem 15

Posted 10/01/2015
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This problem is proposed by Ran Pan. If you want to submit your problem, please click here.

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This problem is about numbers of tilings of a grid by polyominoes.


$a(n)$ is the number of tilings of a $3\times n$ grid by $n$ monominoes and $n$ dominoes.

$b(n)$ is the number of tilings of a $5\times n$ grid by $n$ dominoes and $n$ straight trominoes.

Obviously, $a(1)=b(1)=2$. $a(2)=11$ and they are in pictured in following figure.

Find $a(n)$ and $b(n)$.




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