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 A363512 #25 Jun 12 2023 01:10:14 %S A363512 1,20,1348,353616,446148992,2118502178496,38636185528212416 %N A363512 The number of affine dependencies among the vertices of the n-cube. %C A363512 a(n) is also the number of circuits of any point configuration combinatorially equivalent to a unit cube in dimension n. %H A363512 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 A363512 For n = 2, there is only one affine dependence among the vertices of the square involving all points. %e A363512 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. %Y A363512 Cf. A363506 for the same numbers up to symmetry. Related to A007847 (and A363505, resp.) by oriented-matroid duality. %K A363512 nonn,hard,more %O A363512 2,2 %A A363512 _Jörg Rambau_, Jun 08 2023