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No neighbors allowed (Posted on 2015-05-22) Difficulty: 3 of 5
How many subsets of {1,2,...,n} contain no consecutive integers?

  Submitted by Ady TZIDON    
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Solution: (Hide)
Answer: a(n)=f(n+2); f for Fibonacci number

Solution a(n) must cover all the qualifying subsets of n-1 integers
i.e, a(n-1) plus
all the qualifying subsets of n-2 elements, where to each of them integer n was added (the integer n-1 is absent!).
a(n)= a(n-1) + a(n-2) a(1)=2=f(3) so a(n)=f(n+2)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Hints/Tipsre: solution............spoiler Ady TZIDON2015-05-22 17:28:26
SolutionsolutionCharlie2015-05-22 15:37:25
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