%I A006069 M1903
%S A006069 2,8,96,43008,58018928640
%N A006069 Number of directed Hamiltonian cycles (or Gray codes) on n-cube with 
               a marked starting node.
%C A006069 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.
%D A006069 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006069 M. Gardner, Knotted Doughnuts and Other Mathematical Entertainments. 
               Freeman, NY, 1986, p. 24.
%H A006069 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HamiltonianCircuit.html">Link to a section of The World of Mathematics.</
               a>
%F A006069 a(n)=A003042(n)*2^n. - Max Alekseyev, Jun 15 2006
%e A006069 a(1) = 2: we have 1,2 or 2,1.
%e A006069 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.
%Y A006069 Cf. A003042, A006070, A091299.
%Y A006069 Sequence in context: A001417 A156926 A001697 this_sequence A052457 A119654 
               A008926
%Y A006069 Adjacent sequences: A006066 A006067 A006068 this_sequence A006070 A006071 
               A006072
%K A006069 nonn,more
%O A006069 1,1
%A A006069 N. J. A. Sloane (njas(AT)research.att.com).
%E A006069 a(5) corrected by Jonathan Cross (jcross(AT)wcox.com), Oct 10 2001
%E A006069 Definition corrected by Max Alekseyev, Jun 15 2006