Subsets with no neighbors

MediumCombinatorics~5m

How many subsets of {1,2,…,10}\{1,2,\dots,10\} contain no two consecutive integers (the empty set counts)?

Show hints (2)+
  1. Let ana_n count valid subsets; condition on whether nn is included.
  2. You get Fibonacci: the answer is Fn+2F_{n+2}.

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