%I A006070 M5295
%S A006070 0,0,48,48384,129480729600
%N A006070 Number of Hamiltonian paths on n-cube which are strictly not cycles.
%C A006070 Number of Gray codes of length n which strictly do not close.
%C A006070 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 not adjacent to the first.
%D A006070 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006070 M. Gardner, Knotted Doughnuts and Other Mathematical Entertainments. 
               Freeman, NY, 1986, p. 24.
%H A006070 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HamiltonianPath.html">Link to a section of The World of Mathematics.</
               a>
%e A006070 There are no such paths for n=1 or n=2 (the square). For n = 3 every 
               path has to end at the node of the cube that is diametrically opposite 
               to the start. There are 16 choices for the start and for each start 
               there are 3 Hamiltonian paths that end at the opposite node, so a(3) 
               = 3*16 = 48.
%Y A006070 Cf. A006069, A091299.
%Y A006070 Sequence in context: A164278 A159441 A011787 this_sequence A081262 A008704 
               A037947
%Y A006070 Adjacent sequences: A006067 A006068 A006069 this_sequence A006071 A006072 
               A006073
%K A006070 nonn
%O A006070 1,3
%A A006070 N. J. A. Sloane (njas(AT)research.att.com).
%E A006070 a(5) from Greg Barton (greg_barton(AT)yahoo.com), May 24 2004