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.

1, 3, 123, 14632581

Offset: 1

Author

N. J. A. Sloane, Feb 11 2013

Keywords

• nonn
• bref
• more

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.

Examples

			For n=2 the three figures are: the four edges of a square, or omit one edge, or omit two adjacent edges.
		

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.]
• Andrew Weimholt, 3D solutions in numerical representation
• Andrew Weimholt, Notes on reading the 3D solutions
• Andrew Weimholt, C++ program for A222186 and A222192

Crossrefs

Cf. A222192.

Extensions

a(3) confirmed by Andrew Weimholt, Feb 12 2013

a(4) computed by Andrew Weimholt, Feb 13 2013