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A003043
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Number of Hamiltonian paths (or Gray codes) on n-cube with a marked starting node.
(Formerly M2112)
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4
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OFFSET
| 1,2
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COMMENTS
| 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. The final node may or may not be adjacent to the first. Finally, divide by 2^n since the starting node really doesn't matter.
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REFERENCES
| M. Gardner, Mathematical Games, Sci. Amer. Vol. 228 (No. 4, Apr. 1973), p. 111.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| V. Shevelev, Combinatorial minors of matrix functions and their applications
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FORMULA
| a(n) = A091299(n)/2^n
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CROSSREFS
| Cf. A091299, A006069, A006070, A003042, A066037, A091302.
Sequence in context: A060598 A055687 A006262 * A059783 A191554 A066361
Adjacent sequences: A003040 A003041 A003042 * A003044 A003045 A003046
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KEYWORD
| nonn,more
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| a(5) (from A091299) from Max Alekseyev (maxale(AT)gmail.com), Jul 09 2006
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