1,1

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.

a(7) was found by exhaustive search by Kochut.

Longest closed achordal path in n-dimensional hypercube.

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. 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. W. Davies, Longest "separated" paths and loops in an N cube, IEEE Trans. Electron. Computers, 14 (1965), 261.

V. Klee, What is the maximum length of a d-dimensional snake?, Amer. Math. Monthly, 77 (1970), 63-65.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

D. A. Casella and W. D. Potter, New Lower Bounds for the Snake-in-the-box Problem: Using Evolutionary Techniques to Hunt for Snakes.

Pavel Emelianov, Snake-in-the-box

Krys J. Kochut, Snake-In-The-Box Codes for Dimension 7, Journal of Combinatorial Mathematics and Combinatorial Computing, Vol. 20, pp. 175-185, 1996

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

a(4)=8: Path of a longest 4-coil: 0000 1000 1100 1110 0110 0111 0011 0001 0000. See Figure 1 in Kochut.

Solutions of lengths 4,6,8,14 and 26 in dimensions 2..6 from Arlin Anderson (starship1(AT)gmail.com):

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;

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;

Cf. A099155, length of maximum n-snake.

Sequence in context: A162762 A156097 A039597 this_sequence A167229 A068902 A077569

Adjacent sequences: A000934 A000935 A000936 this_sequence A000938 A000939 A000940

nonn,nice,hard

N. J. A. Sloane (njas(AT)research.att.com).

Edited and extended by Hugo Pfoertner (hugo(AT)pfoertner.org), Oct 13 2004

After 48, lower bounds on the next terms are 96, 180, 344, 630, 1236. - Darren Casella (artdeco42(AT)yahoo.com), Mar 04 2005