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 A364649 #10 Sep 01 2023 04:46:26
%S A364649 1,2,5,7,11,18,28,45,82
%N A364649 Maximal number of pairwise non-orthogonal 1-dimensional subspaces over F_3^n.
%C A364649 Let V=F_p^n be the n-dimensional vector space over the field F_p with p elements, where p is a prime. We call 1-dimensional subspaces <u> and <v> non-orthogonal if the standard scalar product u*v=\sum_{i=1}^n u_iv_i is nonzero. Let G be the graph with the 1-dimensional subspaces as vertices and edges given by pairs of distinct non-orthognal subspaces. It seems difficult to compute the clique number of G. For p=3, a(n) is this clique number. The given values have been computed with GAP.
%e A364649 a(3)=5 by the following vectors: 100,111,112,121,122.
%o A364649 (GAP) LoadPackage("grape");;
%o A364649 p:=3;;
%o A364649 for n in [1..5] do
%o A364649 T:=Filtered(GF(p)^n,v->First(v,x->x<>0*Z(p))=Z(p)^0);; #normalized vectors
%o A364649 g:=Graph(Group(()),T,Permuted,{x,y}->x<>y and x*y<>0*Z(p),true);;
%o A364649 Print(CliqueNumber(g),"\n");
%o A364649 od;
%K A364649 nonn,more
%O A364649 1,2
%A A364649 _Benjamin Sambale_, Jul 31 2023