

A066372


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


2



1, 1, 2, 3, 5, 8, 15, 23, 43, 71, 128, 209, 379, 650, 1145, 1928, 3422, 5908, 10295, 17530, 30738, 53088, 91971, 157194, 273621, 471865, 814557, 1393822, 2414895, 4157492, 7160018, 12253782, 21163410, 36381025, 62549316, 107029982, 184430758
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OFFSET

1,3


COMMENTS

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.


REFERENCES

Deborah Freedman, dlf(AT)alumni.princeton.edu, personal communication.


LINKS

Table of n, a(n) for n=1..37.
Erich Friedman, Illustration of initial terms
Ron Knott, Watch Out for Fibonacci Forgeries  RightAngled Links?
Index entries for sequences obtained by enumerating foldings


EXAMPLE

Let LRUD denote left, right, up, down. Then for n = 1..4 the solutions are R, RD, RDL, RDR, RDLU, RDLD, RDRD.
For n=5 the 5 shapes are:
__.__. __....__ __.... .__.... __......
..__ ..__.. ...__ ..__ ..__...
...... ........ ....... ....... .....__


CROSSREFS

See A001997 for another version.
Cf. A046661, A122224 for selfavoiding paths.
Sequence in context: A104880 A152478 A102973 * A058519 A181065 A282239
Adjacent sequences: A066369 A066370 A066371 * A066373 A066374 A066375


KEYWORD

more,nonn,nice


AUTHOR

Richard D. Plotz (Dick(AT)Plotz.com), Dec 22 2001


EXTENSIONS

a(10)a(23) from Nathaniel Johnston, Jan 04 2011
a(24)a(37) from Bert Dobbelaere, Jan 12 2020


STATUS

approved



