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A066372 Number of different shapes formed by bending a piece of wire of length n in the plane. 2


%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 n-1 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 self-coincident 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/hosted-sites/R.Knott/Fibonacci/fibforgery.html#rightlinks">Watch Out for Fibonacci Forgeries - Right-Angled 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 self-avoiding 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

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Last modified August 11 15:12 EDT 2020. Contains 336428 sequences. (Running on oeis4.)