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I need help with the following problem :

In how many ways we can seat $n$ couples on the two longer sides of a rectangular table such that no couple sits next to each other and facing each other, and people of the same gender do not sit next to each other or facing each other.

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    I guess we're assuming no same-gender couples?2011-10-28

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One approach is to find the answer by hand for $n=4,5,6$, say, then look it up in the Online Encyclopedia of Integer Sequences.