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A363506 revision #11

A363506
The number of affine dependencies among the vertices of the n-cube up to symmetry.
3
1, 3, 15, 186, 12628, 3591868, 3858105362
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 up to symmetry.
EXAMPLE
For n = 2, all vertices of the square constitute the only affine dependence.
For n = 3, there is an affine dependence in each boundary square all of which are equivalent; moreover, there is one affine dependence in each square cutting the cube in half all of which are equivalent; the remaining affine dependence with five elements contains a triangle spanned by all neighbors of a point together with that point and the point opposite to it in the 3-cube.
CROSSREFS
Cf. A363512 for the total numbers (not up to symmetry). Related to A363505 (and A007847, resp.) by oriented-matroid duality.
Sequence in context: A173301 A361053 A260079 * A364075 A087614 A063739
KEYWORD
nonn,hard,more
AUTHOR
Jörg Rambau, Jun 06 2023
STATUS
proposed