Let n be a positive integer. If T is a subset of {1,...,n} we say that T is an n-palindrome if, for every i in {1,...,n}, if i is in T then n+1-i is in T. For instance, {1,2,4,5} is a 5-palindrome, but is not a 6-palindrome. Examples of 6-palindromes include {2,5} and

the empty set. Show with a combinatorial proof that the number of n-palindromes equals 2^(n/2) for n even, and 2^(n+1/2) for n odd. (Hint: A set of cardinality k has 2k subsets.)

the empty set. Show with a combinatorial proof that the number of n-palindromes equals 2^(n/2) for n even, and 2^(n+1/2) for n odd. (Hint: A set of cardinality k has 2k subsets.)

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