cp's OEIS Frontend

A222186 a(n) = number of distinct ways to choose a subset of the n*2^(n-1) edges of the n-cube so that the resulting figure is connected and fully n-dimensional.

%I A222186 #33 Feb 14 2013 14:18:55
%S A222186 1,3,123,14632581
%N A222186 a(n) = number of distinct ways to choose a subset of the n*2^(n-1) edges of the n-cube so that the resulting figure is connected and fully n-dimensional.
%C A222186 "Distinct" means that figures differing by a rotation are not regarded as different.
%C A222186 "Fully n-dimensional" means not lying in a proper subspace.
%C A222186 Suggested by Sol LeWitt's work "Variations of Incomplete Open Cubes," which shows 122 of the 123 figures in the three-dimensional case.
%D A222186 Peter Schjeldahl, Less is beautiful, The Art World, The New Yorker,  March 13, 2000, pp. 98-99.
%H A222186 Sol LeWitt, <a href="http://25.media.tumblr.com/tumblr_masbbafJ4K1rf1adro1_1280.jpg">Variations of Incomplete Open Cubes</a> [The full cube itself is not included in his list.]
%H A222186 Andrew Weimholt, <a href="/A222186/a222186.dat.txt">3D solutions in numerical representation</a>
%H A222186 Andrew Weimholt, <a href="/A222186/a222186_1.dat.txt">Notes on reading the 3D solutions</a>
%H A222186 Andrew Weimholt, <a href="/A222186/a222186.cpp.txt">C++ program for A222186 and A222192</a>
%e A222186 For n=2 the three figures are: the four edges of a square, or omit one edge, or omit two adjacent edges.
%Y A222186 Cf. A222192.
%K A222186 nonn,bref,more
%O A222186 1,2
%A A222186 _N. J. A. Sloane_, Feb 11 2013
%E A222186 a(3) confirmed by _Andrew Weimholt_, Feb 12 2013
%E A222186 a(4) computed by _Andrew Weimholt_, Feb 13 2013