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We have been given n, find total number of ways to form a $3\times n$ board using $2\times 1$ boxes.

thesmallprint
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Sanjit Prasad
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  • I seem to recall this is done in detail in Graham/Knuth/Patashnik's Concrete Mathematics. – Angina Seng Jun 06 '18 at 15:16
  • Welcome to stackexchange. You are more likely to get help if you show us what you tried and where you are stuck. That will also give us some idea of the kind of mathematics you know and might be able to use here. – Ethan Bolker Jun 06 '18 at 15:22
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    If $n \equiv 1\pmod{2}$, then there are zero ways. So, you only need to consider when $n$ even. Next, try to find a recursion relation to figure it out. Let $a_n$ be the number of ways to form the $3\times n$ board and try to see how to form the $3\times (n+2)$ board. – SlipEternal Jun 06 '18 at 15:24
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    See https://math.stackexchange.com/questions/2095276/tiling-dominos-on-a-3x2n-grid – saulspatz Jun 06 '18 at 15:26

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