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 A378400 #12 Jan 01 2025 18:13:25
%S A378400 1,1,2,8,52,676,14463
%N A378400 Number of subsets of {1,2,3,...,n}^2 with the property that every point has exactly two other closest points.
%e A378400 For n=3, the a(3)=8 subsets are
%e A378400 ... oo. .oo ... ... ooo .o. o.o
%e A378400 ... oo. .oo oo. .oo o.o o.o ...
%e A378400 ... ... ... oo. .oo ooo .o. o.o
%e A378400 For n=4, the a(4)=52 subsets include
%e A378400 .o.. .o.. oooo oo.o ..oo ooo.
%e A378400 o.o. ...o o..o oo.. o.oo o.o.
%e A378400 .o.. o... oo.o ..oo .... o.o.
%e A378400 ...o ..o. .ooo ..oo o.o. ooo.
%t A378400 d[p1_,p2_]:=(p1-p2).(p1-p2)
%t A378400 dists[L_,pt_]:=Sort[Map[d[pt,#]&,Complement[L,{pt}]]]
%t A378400 check[L_,pt_]:=(L =={})||((Length[L]>= 3)&&(dists[L,pt][[1]]==dists[L,pt][[2]])&&(dists[L,pt][[2]]< dists[L,pt][[3]]))
%t A378400 check[L_]:=Apply[And,Map[check[L, #]&,L]]
%t A378400 Table[Length[Select[Tuples[Tuples[{0,1},n],n],check[Position[#, 1]]&]],{n,0,5}]
%Y A378400 Cf. A297664.
%K A378400 nonn,hard,more
%O A378400 0,3
%A A378400 _Erich Friedman_, Nov 24 2024
%E A378400 a(6) from _Michael S. Branicky_, Jan 01 2025