A271907 Size of the largest subset S of the points of an n X n square grid such that no three of the points of S form an isosceles triangle.

1, 2, 4, 6, 8, 10, 12, 14, 16, 18

Offset

1,2

Comments

S must not contain 3 points A,B,C such that |AB| = |BC|.

For example, this configuration is forbidden:

O O O B

O O O O

A O O O

O C O O

It appears that this is simply a(n) = 2n-2 for n>1, and if so this entry may be replaced by a comment in A271914 and A271906, and this A-number recycled.

a(11) <= 30, a(12) <= 34, a(13) <= 35. - Chai Wah Wu, Dec 07 2025

Links

Table of n, a(n) for n=1..10.

Example

Illustration for a(3) = 4:
   O X X
   X O O
   X O O
Illustration for a(8) = 14:
   O X X X X X O X
   X O O O O O O X
   X O O O O O O O
   X O O O O O O O
   X O O O O O O O
   X O O O O O O O
   O O O O O O O O
   X X O O O O O O

Crossrefs

Cf. A271906, A227133.

Main diagonal of A271914.

Sequence in context: A319747 A055958 A241142 * A069816 A088116 A100817

Adjacent sequences: A271904 A271905 A271906 * A271908 A271909 A271910

Keyword

nonn,more

Author

Giovanni Resta and N. J. A. Sloane, Apr 22 2016

Status

approved