A338354 A (0,1)-matrix in the first quadrant read by downward antidiagonals: an example of a uniformly recurrent 2-D word in which row 0 is non-recurrent.

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

Offset

0

Comments

Proposition 5 of Charlier et al. (2020) gives the formal definition of the matrix.

References

Charlier, Émilie, Svetlana Puzynina, and Élise Vandomme. "Recurrence along directions in multidimensional words." Discrete Mathematics 343.10 (2020): 112006.

Links

Table of n, a(n) for n=0..54.

Émilie Charlier, Svetlana Puzynina, and Élise Vandomme, Recurrence along directions in multidimensional words, arXiv:1907.00192 [math.CO], 2019-2020.

Example

The array begins:
...........
1 1 1 1 1 1 1 1 1 1 1 1 ...
1 0 0 0 1 0 0 0 1 0 0 0 ...
1 1 1 1 1 1 1 1 1 1 1 1 ...
1 0 1 0 1 0 1 0 1 0 1 0 ...
1 1 1 1 1 1 1 1 1 1 1 1 ...
1 0 0 0 0 0 0 0 1 0 0 0 ...
1 1 1 1 1 1 1 1 1 1 1 1 ...
1 0 1 0 1 0 1 0 1 0 1 0 ...
1 1 1 1 1 1 1 1 1 1 1 1 ...
1 0 0 0 1 0 0 0 1 0 0 0 ...
1 1 1 1 1 1 1 1 1 1 1 1 ...
1 0 1 0 1 0 1 0 1 0 1 0 ...
1 1 1 1 1 1 1 1 1 1 1 1 ...
1 0 0 0 0 0 0 0 0 0 0 0 ...
This is to be read from bottom to top and left to right.
The initial antidiagonals (starting in bottom left corner)  are:
1,
1,0,
1,1,0,
1,0,1,0,
1,1,1,1,0,
1,0,1,0,1,0,
1,1,0,1,1,1,0,
1,0,1,0,1,0,1,0,
1,1,1,1,1,1,1,1,0,
1,0,1,0,1,0,1,0,1,0,
...

Crossrefs

Cf. A338353.

Sequence in context: A215200 A054521 A349221 * A014240 A014471 A230002

Adjacent sequences: A338351 A338352 A338353 * A338355 A338356 A338357

Keyword

nonn,tabl,more

Author

N. J. A. Sloane, Nov 02 2020

Status

approved