Search: id:A001997
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%I A001997 M1206 N0465
%S A001997 1,1,2,4,10,24,66,176,493,1362,3821,10660,29864,83329,232702,648182,
%T A001997 1804901,5015725,13931755,38635673,107090666,296449133,820271143,
%U A001997 2267225157,6264244414,17291930470
%N A001997 Different shapes formed by bending a piece of wire of length n in the 
               plane.
%C A001997 Wire is marked into n equal segments by n-1 marks, is bent at right angles 
               at each of one or more of these points, making each segment parallel 
               to one of two rectangular axes. (Stays in plane, bends are of 0 or 
               +-90 degs.) May cross itself but is not self-coincident over a finite 
               length.
%C A001997 A trail is a path which may cross itself but does not reuse an edge. 
               This sequence counts undirected trails on the square lattice up to 
               rotation and reflection. Directed trails are counted by A006817.
%D A001997 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001997 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001997 R. M. Foster, Solution to Problem E185, Amer. Math. Monthly, 44 (1937), 
               50-51.
%H A001997 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Self-AvoidingWalk.html">Link to a section of The World of Mathematics.</
               a>
%H A001997 <a href="Sindx_Fo.html#fold">Index entries for sequences obtained by 
               enumerating foldings</a>
%e A001997 ._. ._._._. Here are the
%e A001997 |_. . ._. . 4 solutions
%e A001997 ._._| . |_. when n=3 (described by 00, RR, 0L, RL).
%e A001997 The 24 solutions for n=5 are 0000, 000R, 00R0, 00RR, 00RL, L00L, L00R, 
               0R0R, 0R0L, 0RR0, 0RL0, 0LRL, 0LRR, 0LLR, 0LLL, R0LR, R0LL, R0RL, 
               R0RR, LRLR, LRLL, LRLR, LRRR, LLRR.
%Y A001997 Total number of different shapes (including those shapes where the wire 
               is self-coincident over a finite path) is A001998.
%Y A001997 Sequence in context: A137842 A049146 A000682 this_sequence A000084 A057734 
               A003104
%Y A001997 Adjacent sequences: A001994 A001995 A001996 this_sequence A001998 A001999 
               A002000
%K A001997 nonn,more,nice,walk
%O A001997 0,3
%A A001997 N. J. A. Sloane (njas(AT)research.att.com).
%E A001997 More terms from David W. Wilson (davidwwilson(AT)comcast.net), Jul 18 
               2001
%E A001997 Much less is known about the three-dimensional problem.

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