%I
%S 1,1,2,3,5,8,15,23,43,71,128,209,379,650,1145,1928,3422,5908,10295,
%T 17530,30738,53088,91971,157194,273621,471865,814557,1393822,2414895,
%U 4157492,7160018,12253782,21163410,36381025,62549316,107029982,184430758
%N Number of different shapes formed by bending a piece of wire of length n in the plane.
%C Wire is marked into n equal segments by n1 marks, is bent at right angles at each of these points, making each segment parallel to one of two rectangular axes. (Stays in plane, bends are of +90 degs.) May cross itself but is not selfcoincident over a finite length. Two configurations which differ only in a rotation or turning over are not counted as different.
%D Deborah Freedman, dlf(AT)alumni.princeton.edu, personal communication.
%H Erich Friedman, <a href="/A066372/a066372.gif">Illustration of initial terms</a>
%H Ron Knott, <a href="http://www.maths.surrey.ac.uk/hostedsites/R.Knott/Fibonacci/fibforgery.html#rightlinks">Watch Out for Fibonacci Forgeries  RightAngled Links?</a>
%H <a href="/index/Fo#fold">Index entries for sequences obtained by enumerating foldings</a>
%e Let LRUD denote left, right, up, down. Then for n = 1..4 the solutions are R, RD, RDL, RDR, RDLU, RDLD, RDRD.
%e For n=5 the 5 shapes are:
%e __.__. __....__ __.... .__.... __......
%e ..__ ..__.. ...__ ..__ ..__...
%e ...... ........ ....... ....... .....__
%Y See A001997 for another version.
%Y Cf. A046661, A122224 for selfavoiding paths.
%K more,nonn,nice
%O 1,3
%A Richard D. Plotz (Dick(AT)Plotz.com), Dec 22 2001
%E a(10)a(23) from _Nathaniel Johnston_, Jan 04 2011
%E a(24)a(37) from _Bert Dobbelaere_, Jan 12 2020
