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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.
2
1, 3, 123, 14632581
OFFSET
1,2
COMMENTS
"Distinct" means that figures differing by a rotation are not regarded as different.
"Fully n-dimensional" means not lying in a proper subspace.
Suggested by Sol LeWitt's work "Variations of Incomplete Open Cubes," which shows 122 of the 123 figures in the three-dimensional case.
REFERENCES
Peter Schjeldahl, Less is beautiful, The Art World, The New Yorker, March 13, 2000, pp. 98-99.
LINKS
Sol LeWitt, Variations of Incomplete Open Cubes [The full cube itself is not included in his list.]
EXAMPLE
For n=2 the three figures are: the four edges of a square, or omit one edge, or omit two adjacent edges.
CROSSREFS
Cf. A222192.
Sequence in context: A012569 A078258 A258658 * A124246 A219010 A037118
KEYWORD
nonn,bref,more
AUTHOR
N. J. A. Sloane, Feb 11 2013
EXTENSIONS
a(3) confirmed by Andrew Weimholt, Feb 12 2013
a(4) computed by Andrew Weimholt, Feb 13 2013
STATUS
approved