

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
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OFFSET

0,4


COMMENTS

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.


LINKS

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.


CROSSREFS



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



