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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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.

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 - Right-Angled 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 self-avoiding 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

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Last modified July 7 16:01 EDT 2020. Contains 335496 sequences. (Running on oeis4.)