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

0,3

Links

Table of n, a(n) for n=0..6.

Example

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.

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}]

Crossrefs

Cf. A297664.

Sequence in context: A349012 A057629 A191507 * A191602 A145157 A323871

Adjacent sequences: A378397 A378398 A378399 * A378401 A378402 A378403

Keyword

nonn,hard,more

Author

Erich Friedman, Nov 24 2024

Extensions

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

Status

approved