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Search: id:A061714
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| A061714 |
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Number of types of (n-1)-swap moves for traveling salesman problem. Number of circular permutations on elements 0,1,...,2n-1 where every two elements 2i,2i+1 and no two elements 2i-1,2i are adjacent. |
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+0
4
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| 1, 0, 1, 4, 25, 208, 2121, 25828, 365457, 5895104, 106794993, 2147006948, 47436635753, 1142570789072, 29797622256377, 836527783016196, 25153234375160993, 806519154686509056, 27470342073410272609
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OFFSET
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0,4
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COMMENT
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An n-swap move consists of the removal of n edges and addition of n different edges which result in a new tour. The type can be characterized by how the n segments of the original tour formed by the removal are reassembled.
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FORMULA
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a(n) = (-1)^n + Sum_{i=0..n-1} (-1)^(n-1-i)*C(n,i+1)*i!*2^i = (-1)^n + A120765(n)
E.g.f.: exp(-x)*(1-ln(1-2x)/2)
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CROSSREFS
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Cf. A001171 (sequential n-swap moves).
Sequence in context: A088159 A036242 A120955 this_sequence A005411 A105628 A064299
Adjacent sequences: A061711 A061712 A061713 this_sequence A061715 A061716 A061717
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KEYWORD
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nonn,nice
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AUTHOR
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David Applegate (david(AT)research.att.com), Jun 21 2001
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EXTENSIONS
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Revised by Max Alekseyev (maxal(AT)cs.ucsd.edu), Jul 03 2006
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