This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A363505 #20 Jun 08 2023 10:57:42 %S A363505 2,3,6,15,63,623,22432,3899720 %N A363505 Number of hyperplanes spanned by the vertices of an n-cube up to symmetry. %C A363505 a(n) is also the number of cocircuits of any point configuration combinatorially equivalent to the unit cube in dimension n up to symmetry. %H A363505 Jörg Rambau, <a href="https://www.wm.uni-bayreuth.de/de/team/rambau_joerg/TOPCOM/SymLexSubsetRS.pdf">Symmetric lexicographic subset reverse search for the enumeration of circuits, cocircuits, and triangulations up to symmetry</a>, Manuscript distributed with <a href="https://www.wm.uni-bayreuth.de/de/team/rambau_joerg/TOPCOM/">TOPCOM</a>. %e A363505 For n = 2, it can be seen that there are only two non-equivalent hyperplanes spanned by vertices of the square: one spanned by a boundary edge having all remaining points on one side and one spanned by a diagonal separating the remaining points. %e A363505 For n = 3, we again have a hyperplane parallel to a coordinate plane spanned by a boundary square having all the remaining points on one side; moreover, a hyperplane spanned by the four points on the opposite axis-parallel parallel boundary edges of two opposite boundary squares leaving two remaining points on either side, and a skew hyperplane spanned by the three neighbors of a single point separating that point from the remaining points. %Y A363505 A007847 gives the total numbers (not up to symmetry). Related to A363506 (and A363512, resp.) by oriented-matroid duality. %K A363505 nonn,hard,more %O A363505 2,1 %A A363505 _Jörg Rambau_, Jun 06 2023