A280538 Number of essentially different optimal solutions for the n X n X n "No four in plane" problem.

1, 1, 232, 38, 36

Offset

2,3

Comments

a(7) >= 3885, with an estimated value of about 5500.

Links

Table of n, a(n) for n=2..6.

Ed Pegg, No-Four-In-Plane, can 11 points be picked from a 4 X 4 X 4 grid?. Question in Mathematics Stack Exchange, Configurations corresponding to a(4) and a(5) provided in answers.

Walter Möhres and Hugo Pfoertner, 36 optimal solutions for the 6 X 6 X 6 "No four in plane" problem.

Example

a(2)=1, because there exists only one normalized configuration (removing rotations and reflections) with A280537(2)=5 points: (0,0,0),(0,0,1),(0,1,0),(1,0,0),(1,1,1).
a(3)=1, because there exists only one normalized configuration with A280537(3)=8 points: (0,0,0),(0,1,1),(0,1,2),(1,0,1),(1,1,0),(1,2,0),(2,0,1),(2,2,2).

Crossrefs

Cf. A280537 for links and references.

Sequence in context: A359011 A172935 A319306 * A050423 A126818 A277076

Adjacent sequences: A280535 A280536 A280537 * A280539 A280540 A280541

Keyword

nonn,hard,more

Author

Hugo Pfoertner, Jan 05 2017

Status

approved