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A271771
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Maximum total Hamming distance between pairs of consecutive elements in any permutation of all 2^n binary words of length n.
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2
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1, 5, 18, 53, 140, 347, 826, 1913, 4344, 9719, 21494, 47093, 102388, 221171, 475122, 1015793, 2162672, 4587503, 9699310, 20447213, 42991596, 90177515, 188743658, 394264553, 822083560, 1711276007, 3556769766, 7381975013, 15300820964, 31675383779
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = n*2^n - 2^(n-1) - n + 1.
G.f.: x*(1 + 2*x)/(1-2*x)^2 - x^2/(1-x)^2.
E.g.f.: (2*x - 1/2)*exp(2*x) + (1 - x)*exp(x) - 1/2. (End)
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EXAMPLE
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Example: for n=3 the sequence 000 111 001 110 011 100 010 101 has total hamming distance 3+2+3+2+3+2+3 = 18.
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MAPLE
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MATHEMATICA
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PROG
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(C) unsigned a(unsigned n) { return n*(1<<n) - (1<<(n-1)) - n + 1; }
(Magma) [n*2^n - 2^(n-1) - n + 1: n in [1..50]]; // Wesley Ivan Hurt, Apr 18 2016
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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