Chairs in a row: The Teachers version

This time we have n chairs in a row and a roomful of people.
If you've ever been to a gathering where there are teachers present, you will know they always talk about their school/college (boring!). So we will insist that no two teachers should sit next to each other along a row of seats and count how many ways we can seat n people, if some are teachers (who cannot be next to each other) and some are not .

There will always be a relation between number of ways for a given number of chairs, if no two teachers are allowed to sit next to each other!
what is that relation.


  1. no. of ways will be
    2*(n/2)! if n is even
    2*(n+1/2)! if n is odd

  2. @navin can you please elaborate with the data that you have calculated for n=1,2,3 etc.


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