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 A003043 Number of Hamiltonian paths (or Gray codes) on n-cube with a marked starting node. (Formerly M2112) 5
 1, 2, 18, 5712, 5859364320 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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. Also, the number of strings s of length 2^n - 1 over the alphabet {1,2,...,n} with the property that every contiguous subblock has some letter that appears an odd number of times. 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). LINKS V. Shevelev, Combinatorial minors of matrix functions and their applications, arXiv:1105.3154 [math.CO], 2011-2014. V. Shevelev, Combinatorial minors of matrix functions and their applications, Zesz. Nauk. PS., Mat. Stosow., Zeszyt 4, pp. 5-16. (2014). FORMULA a(n) = A091299(n)/2^n. CROSSREFS Cf. A091299, A006069, A006070, A003042, A066037, A091302, A179926. Sequence in context: A060598 A055687 A006262 * A059783 A208056 A276092 Adjacent sequences:  A003040 A003041 A003042 * A003044 A003045 A003046 KEYWORD nonn,hard,more AUTHOR EXTENSIONS a(5) (from A091299) from Max Alekseyev, Jul 09 2006 Alternative description added by Jeffrey Shallit, Feb 02 2013 STATUS approved

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