Problematic little chairs

There are \( 2016 \) chairs in a row and two available colours, blue and red. On how many ways can we paint all chairs, so that number of blue chairs is even?

(e. g. A case in which the first two chairs are blue and other are red, is different from the case in which the last two chairs are blue and other are red)

In solution section "inspiration" for the problem is mentioned.

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