%I #12 Aug 12 2018 17:13:28
%S 0,0,1,8,22,256,2247,21576,225102,2303014,24563283,267169300,
%T 2937239494,32814269626,370231763542,4215902111928
%N 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).
%C 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.
%C Richard Gordon from the University of Manitoba (GordonR(AT)ms.umanitoba.ca) first raised the question of how many wurfels there are.
%H Richard Gordon, Martin M. Hanczyc, Nikolai D. Denkov, Mary A. Tiffany, Stoyan K. Smoukov, <a href="https://doi.org/10.1016/B9780128119402.000186">"Emergence of Polygonal Shapes in Oil Droplets and Living Cells: The Potential Role of Tensegrity in the Origin of Life"</a>, 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.
%K nonn,more
%O 0,4
%A _John Tromp_, Apr 06 2006
%E a(15) from _John Tromp_, May 05 2006
