A267188 Square array read by antidiagonals: T(i,j) = A267181(i,j) mod 2, with i >= 0, j >= 0.

0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1

Offset

0

Comments

Constructed in a (failed) attempt to find an infinite array of 0's and 1's containing no square (oriented parallel to the axes) in which all four vertices are labeled 0. Such an array would lead to a lower bound on the "red-dot" problem in A227133. Unfortunately, this array does contain such squares, although they are relatively scarce.

Links

Table of n, a(n) for n=0..106.

Example

The array begins:
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, ...
1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, ...
1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, ...
1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, ...
1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, ...
1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, ...
1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, ...
1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, ...
1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, ...
1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, ...
1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, ...
1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, ...
...
The first few antidiagonals are:
0,
1, 0,
1, 0, 0,
1, 0, 1, 0,
1, 1, 0, 0, 0,
1, 0, 0, 1, 1, 0,
1, 1, 0, 0, 1, 0, 0,
1, 0, 1, 1, 0, 0, 1, 0,
1, 1, 1, 0, 0, 1, 0, 0, 0,
1, 0, 0, 0, 0, 1, 1, 1, 1, 0,
1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0,
...

Crossrefs

Cf. A227133, A267181.

Sequence in context: A241575 A285684 A163538 * A154104 A187976 A197879

Adjacent sequences: A267185 A267186 A267187 * A267189 A267190 A267191

Keyword

nonn,tabl

Author

N. J. A. Sloane, Jan 17 2016

Status

approved