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A117613 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). 0
0, 0, 1, 8, 22, 256, 2247, 21576, 225102, 2303014, 24563283, 267169300, 2937239494, 32814269626, 370231763542, 4215902111928 (list; graph; refs; listen; history; text; internal format)



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.


Table of n, a(n) for n=0..15.

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.


Sequence in context: A131622 A217275 A183308 * A215740 A304177 A306834

Adjacent sequences:  A117610 A117611 A117612 * A117614 A117615 A117616




John Tromp, Apr 06 2006


a(15) from John Tromp, May 05 2006



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Last modified August 9 13:57 EDT 2020. Contains 336323 sequences. (Running on oeis4.)