A378400 Number of subsets of {1,2,3,...,n}^2 with the property that every point has exactly two other closest points.

1, 1, 2, 8, 52, 676, 14463

Offset: 0

Author

Erich Friedman, Nov 24 2024

Keywords

• nonn
• hard
• more

Examples

			For n=3, the a(3)=8 subsets are
  ...  oo.  .oo  ...  ...  ooo  .o.  o.o
  ...  oo.  .oo  oo.  .oo  o.o  o.o  ...
  ...  ...  ...  oo.  .oo  ooo  .o.  o.o
For n=4, the a(4)=52 subsets include
  .o..  .o..  oooo  oo.o  ..oo  ooo.
  o.o.  ...o  o..o  oo..  o.oo  o.o.
  .o..  o...  oo.o  ..oo  ....  o.o.
  ...o  ..o.  .ooo  ..oo  o.o.  ooo.
		

Crossrefs

Cf. A297664.

Programs

Mathematica

d[p1_,p2_]:=(p1-p2).(p1-p2)
dists[L_,pt_]:=Sort[Map[d[pt,#]&,Complement[L,{pt}]]]
check[L_,pt_]:=(L =={})||((Length[L]>= 3)&&(dists[L,pt][[1]]==dists[L,pt][[2]])&&(dists[L,pt][[2]]< dists[L,pt][[3]]))
check[L_]:=Apply[And,Map[check[L, #]&,L]]
Table[Length[Select[Tuples[Tuples[{0,1},n],n],check[Position[#, 1]]&]],{n,0,5}]

Extensions

a(6) from Michael S. Branicky, Jan 01 2025