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A117613
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The number of 3D configurations of a labeled size 2*n "wurfel". A wurfel consists of a series of cubes held together on a looped string such that the string makes a right angle inside each cube. Ignoring the labels would make a wurfel a special kind of polycube in which the cubes can be cyclically ordered at consecutive right angles (equivalently, avoiding 3 consecutive collinear cubes).
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0
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0, 0, 1, 8, 22, 256, 2247, 21576, 225102, 2303014, 24563283, 267169300, 2937239494, 32814269626, 370231763542, 4215902111928
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history;
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OFFSET
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0,4
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COMMENTS
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a(2)=1 since a loop of 2*2=4 labeled cubes has only 1 possible 3D shape. A C program for computing the sequence is available on request.
Richard Gordon from the University of Manitoba (GordonR(AT)ms.umanitoba.ca) first raised the question of how many wurfels there are.
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LINKS
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Richard Gordon, Martin M. Hanczyc, Nikolai D. Denkov, Mary A. Tiffany, Stoyan K. Smoukov, "Emergence of Polygonal Shapes in Oil Droplets and Living Cells: The Potential Role of Tensegrity in the Origin of Life", Habitability of the Universe before Earth, Vol. 1 of the series Astrobiology: Exploring Life on Earth and Beyond, first edition, Richard Gordon, Alexei A. Sharov editors, Elsevier, 2017, p. 487.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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