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A066372
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Number of different shapes formed by bending a piece of wire of length n in the plane.
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2
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1, 1, 2, 3, 5, 8, 15, 23, 43, 71, 128, 209, 379, 650, 1145, 1928, 3422, 5908, 10295, 17530, 30738, 53088, 91971
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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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.
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REFERENCES
| Deborah Freedman, dlf(AT)alumni.princeton.edu, personal communication.
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LINKS
| R. Knott, Watch Out for Fibonacci Forgeries - Right-Angled Links?
Index entries for sequences obtained by enumerating foldings
Erich Friedman, Illustration of initial terms
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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
__.__. __....__ |__.... .__.... __......
..|__| ..|__|.. ...|__| |..|__| ..|__...
...... ........ ....... ....... .....|__
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CROSSREFS
| See A001997 for another version.
Sequence in context: A104880 A152478 A102973 * A058519 A181065 A191792
Adjacent sequences: A066369 A066370 A066371 * A066373 A066374 A066375
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KEYWORD
| more,nonn,nice
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AUTHOR
| Richard D. Plotz (Dick(AT)Plotz.com), Dec 22 2001
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EXTENSIONS
| a(10)-a(23) from Nathaniel Johnston (nathaniel(AT)nathanieljohnston.com), Jan 04 2011
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