%I A003042 M2053
%S A003042 1,2,12,2688,1813091520
%N A003042 Number of directed Hamiltonian cycles (or Gray codes) on n-cube.
%C A003042 Finding a(6) is problem 43 in the Knuth reference. a(6) was estimated 
               to be about 7*10^22 by Silverman, et al.
%D A003042 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A003042 M. Gardner, Knotted Doughnuts and Other Mathematical Entertainments. 
               Freeman, NY, 1986, p. 24.
%D A003042 D. E. Knuth, The Art of Computer Programming, vol. 4A, Combinatorial 
               Algorithms, (to appear), section 7.2.1.1.
%D A003042 Silverman, Jerry; Vickers, Virgil E.; and Sampson, John L., Statistical 
               estimates of the n-bit Gray codes by restricted random generation 
               of permutations of 1 to 2^n, IEEE Trans. Inform. Theory 29 (1983), 
               no. 6, 894-901.
%H A003042 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HamiltonianCircuit.html">Hamiltonian Circuit</a>
%F A003042 a(n) = 2 * A066037(n).
%Y A003042 Equals A006069 divided by 2^n. Cf. A006070, A091299, A003043.
%Y A003042 Cf. A091302.
%Y A003042 Sequence in context: A090904 A125295 A050649 this_sequence A000887 A118542 
               A007155
%Y A003042 Adjacent sequences: A003039 A003040 A003041 this_sequence A003043 A003044 
               A003045
%K A003042 nonn,nice
%O A003042 1,2
%A A003042 N. J. A. Sloane (njas(AT)research.att.com).