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Problem 14

Posted 09/03/2015
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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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In Exercise T, we are looking for number of triangles on $3\times n$ grid.

This problem is about quadrilaterals instead of triangles.

$a(n)$ is the number of simple quadrilaterals on $3\times n$ grid. $b(n)$ is the number of convex quadrilaterals on $3\times n$ grid.

Clearly, $a(1)=b(1)=0$ and $a(2)=b(2)=9$.

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







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