Search: id:A000937
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%I A000937 M0995 N0373
%S A000937 2,4,6,8,14,26,48
%N A000937 Length of longest simple cycle without chords in the n-dimensional hypercube 
               graph. Also called n-coil or closed n-snake-in-the-box problem.
%C A000937 This sequence actually gives the length of a longest closed chordless 
               path in the n-dimensional hypercube. To distinguish closed and open 
               paths, newer terminology uses "n-coil" for closed and "n-snake" for 
               open paths. See also A099155.
%C A000937 a(7) was found by exhaustive search by Kochut.
%C A000937 Longest closed achordal path in n-dimensional hypercube.
%D A000937 D. Casella and W. D. Potter, "New Lower Bounds for the Snake-in-the-box 
               Problem: Using Evolutionary Techniques to Hunt for Snakes". To appear 
               in 18th International FLAIRS Conference, 2005.
%D A000937 D. Casella and W. D. Potter, "New Lower Bounds for the Snake-in-the-box 
               Problem: Using Evolutionary Techniques to Hunt for Coils". Submitted 
               to IEEE Conference on Evolutionary Computing, 2005.
%D A000937 D. W. Davies, Longest "separated" paths and loops in an N cube, IEEE 
               Trans. Electron. Computers, 14 (1965), 261.
%D A000937 V. Klee, What is the maximum length of a d-dimensional snake?, Amer. 
               Math. Monthly, 77 (1970), 63-65.
%D A000937 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000937 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A000937 D. A. Casella and W. D. Potter, <a href="http://www.cs.uga.edu/~potter/
               CompIntell/SnakePaper94.pdf">New Lower Bounds for the Snake-in-the-box 
               Problem: Using Evolutionary Techniques to Hunt for Snakes</a>.
%H A000937 Pavel Emelianov, <a href="http://192.168.216.81/epg/snake.html">Snake-in-the-box</
               a>
%H A000937 Krys J. Kochut, <a href="http://www.cs.uga.edu/~potter/CompIntell/kochut.pdf">
               Snake-In-The-Box Codes for Dimension 7</a>, Journal of Combinatorial 
               Mathematics and Combinatorial Computing, Vol. 20, pp. 175-185, 1996
%H A000937 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Snake.html">Link to a section of The World of Mathematics.</a>
%e A000937 a(4)=8: Path of a longest 4-coil: 0000 1000 1100 1110 0110 0111 0011 
               0001 0000. See Figure 1 in Kochut.
%e A000937 Solutions of lengths 4,6,8,14 and 26 in dimensions 2..6 from Arlin Anderson 
               (starship1(AT)gmail.com):
%e A000937 0 1 3 2; 0 1 3 7 6 4; 1 3 7 6 14 10 8; 0 1 3 7 6 14 10 26 27 25 29 21 
               20 16;
%e A000937 0 1 3 7 6 14 10 26 27 25 29 21 53 37 36 44 40 41 43 47 63 62 54 50 48 
               16;
%Y A000937 Cf. A099155, length of maximum n-snake.
%Y A000937 Sequence in context: A162762 A156097 A039597 this_sequence A167229 A068902 
               A077569
%Y A000937 Adjacent sequences: A000934 A000935 A000936 this_sequence A000938 A000939 
               A000940
%K A000937 nonn,nice,hard
%O A000937 1,1
%A A000937 N. J. A. Sloane (njas(AT)research.att.com).
%E A000937 Edited and extended by Hugo Pfoertner (hugo(AT)pfoertner.org), Oct 13 
               2004
%E A000937 After 48, lower bounds on the next terms are 96, 180, 344, 630, 1236. 
               - Darren Casella (artdeco42(AT)yahoo.com), Mar 04 2005

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