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A267188 Square array read by antidiagonals: T(i,j) = A267181(i,j) mod 2, with i >= 0, j >= 0. 1

%I

%S 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,

%T 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,

%U 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

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

%C 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.

%e The array begins:

%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...

%e 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, ...

%e 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, ...

%e 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, ...

%e 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, ...

%e 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, ...

%e 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, ...

%e 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, ...

%e 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, ...

%e 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, ...

%e 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, ...

%e 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, ...

%e 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, ...

%e ...

%e The first few antidiagonals are:

%e 0,

%e 1, 0,

%e 1, 0, 0,

%e 1, 0, 1, 0,

%e 1, 1, 0, 0, 0,

%e 1, 0, 0, 1, 1, 0,

%e 1, 1, 0, 0, 1, 0, 0,

%e 1, 0, 1, 1, 0, 0, 1, 0,

%e 1, 1, 1, 0, 0, 1, 0, 0, 0,

%e 1, 0, 0, 0, 0, 1, 1, 1, 1, 0,

%e 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0,

%e ...

%Y Cf. A227133, A267181.

%K nonn,tabl

%O 0

%A _N. J. A. Sloane_, Jan 17 2016

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Last modified October 20 09:24 EDT 2021. Contains 348100 sequences. (Running on oeis4.)