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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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..4.

Sol LeWitt, Variations of Incomplete Open Cubes [The full cube itself is not included in his list.]

Andrew Weimholt, 3D solutions in numerical representation

Andrew Weimholt, Notes on reading the 3D solutions

Andrew Weimholt, C++ program for A222186 and A222192

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

Adjacent sequences:  A222183 A222184 A222185 * A222187 A222188 A222189

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

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Last modified November 17 00:08 EST 2019. Contains 329209 sequences. (Running on oeis4.)