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Search: id:A006069
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| A006069 |
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Number of directed Hamiltonian cycles (or Gray codes) on n-cube with a marked starting node.
(Formerly M1903)
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+0
7
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OFFSET
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1,1
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COMMENT
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More precisely, this is the number of ways of making a list of the 2^n nodes of the n-cube, with a distinguished starting position and a direction, such that each node is adjacent to the previous one and the last node is adjacent to the first.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
M. Gardner, Knotted Doughnuts and Other Mathematical Entertainments. Freeman, NY, 1986, p. 24.
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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a(n)=A003042(n)*2^n. - Max Alekseyev, Jun 15 2006
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EXAMPLE
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a(1) = 2: we have 1,2 or 2,1.
a(2) = 8: label the nodes 1, 2, ..., 4. Then the 8 possibilities are 1,2,3,4; 1,4,3,2; 2,3,4,1; 2,1,4,3; etc.
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CROSSREFS
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Cf. A003042, A006070, A091299.
Sequence in context: A001417 A156926 A001697 this_sequence A052457 A119654 A008926
Adjacent sequences: A006066 A006067 A006068 this_sequence A006070 A006071 A006072
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KEYWORD
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nonn,more
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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a(5) corrected by Jonathan Cross (jcross(AT)wcox.com), Oct 10 2001
Definition corrected by Max Alekseyev, Jun 15 2006
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