%I A066037
%S A066037 1,1,6,1344,906545760
%N A066037 Number of Hamiltonian cycles in the binary n-cube, or the number of cyclic 
               n-bit Gray codes.
%C A066037 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; and then dividing the total by 2^(n+1) because the 
               starting node and the direction do not really matter.
%C A066037 The number is a multiple of n!/2 since any directed cycle starting from 
               0^n induces a permutation on the n bits, namely the order in which 
               they first get set to 1.
%D A066037 R. J. Douglas, Bounds on the number of Hamiltonian circuits in the n-cube, 
               Discrete Mathematics, 17 (1977), 143-146.
%D A066037 Harary, Hayes and Wu, A survey of the theory of hypercube graphs, Computers 
               and Mathematics with Applications, 15(4), 1988, 7-289.
%e A066037 The 2-cube has a single cycle consisting of all 4 edges.
%Y A066037 Equals A006069/2^(n+1) and A003042/2.
%Y A066037 Cf. A006070, A091299, A003043, A091302.
%Y A066037 Sequence in context: A013738 A076781 A055306 this_sequence A107252 A131453 
               A160226
%Y A066037 Adjacent sequences: A066034 A066035 A066036 this_sequence A066038 A066039 
               A066040
%K A066037 nonn,nice
%O A066037 1,3
%A A066037 John Tromp (tromp(AT)cwi.nl), Dec 12 2001