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A363512
The number of affine dependencies among the vertices of the n-cube.
3
1, 20, 1348, 353616, 446148992, 2118502178496, 38636185528212416
OFFSET
2,2
COMMENTS
a(n) is also the number of circuits of any point configuration combinatorially equivalent to a unit cube in dimension n.
EXAMPLE
For n = 2, there is only one affine dependence among the vertices of the square involving all points.
For n = 3, since there are 6 embeddings of the square into the boundary and 6 embeddings of the square into the interior of the 3-cube, there are 12 affine dependences on squares; moreover, there is an affine dependence for each of the 8 vertices of the 3-cube coming from the intersection of the line from that vertex to the vertex opposite in the 3-cube with the triangle spanned by the neighbors of that vertex; this adds up to a total of 20 affine dependencies.
CROSSREFS
Cf. A363506 for the same numbers up to symmetry. Related to A007847 (and A363505, resp.) by oriented-matroid duality.
Sequence in context: A229476 A177597 A127847 * A193309 A177601 A200900
KEYWORD
nonn,hard,more
AUTHOR
Jörg Rambau, Jun 08 2023
STATUS
approved