%I A003043 M2112
%S A003043 1,2,18,5712,5859364320
%N A003043 Number of Hamiltonian paths (or Gray codes) on n-cube with a marked starting 
               node.
%C A003043 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.
%D A003043 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A003043 M. Gardner, Mathematical Games, Sci. Amer. Vol. 228 (No. 4, Apr. 1973), 
               p. 111.
%F A003043 a(n) = A091299(n)/2^n
%Y A003043 Cf. A091299(n), A006069, A006070, A003042, A066037, A091302.
%Y A003043 Sequence in context: A060598 A055687 A006262 this_sequence A059783 A066361 
               A120929
%Y A003043 Adjacent sequences: A003040 A003041 A003042 this_sequence A003044 A003045 
               A003046
%K A003043 nonn,more
%O A003043 1,2
%A A003043 N. J. A. Sloane (njas(AT)research.att.com).
%E A003043 a(5) (from A091299) from Max Alekseyev (maxale(AT)gmail.com), Jul 09 
               2006