login
A267188
Square array read by antidiagonals: T(i,j) = A267181(i,j) mod 2, with i >= 0, j >= 0.
1
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.
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
Sequence in context: A241575 A285684 A163538 * A154104 A187976 A197879
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Jan 17 2016
STATUS
approved