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A331104
Consider an empty square array visited by antidiagonals downwards; when the current square is empty, place a 1 X 1 tile or a 1 X 2 tile on it (without overlapping any prior tile) such that the RUNS transform of the sequence of tile widths as they are placed on the grid equals the sequence of tile widths as they are visited; first place a 1 X 1 tile. This sequence corresponds to the tile widths as they are placed.
2
1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2
OFFSET
1,2
COMMENTS
The RUNS transform of this sequence gives A331034.
Is the density of 1's equal to 1/2?
EXAMPLE
The following table read by antidiagonals downwards gives the current sequence:
+---+-------+---+---+-------+---+---+---
| 1 | 2 | 1 | 1 | 2 | 1 | 1 | 2 ...
+---+---+---+---+---+---+---+---+---+---
| 2 | 2 | 2 | 2 | 1 | 1 ...
+---+---+---+---+---+---+---+---+---+---
| 1 | 2 | 1 | 1 | 2 | 1 | 2 ...
+---+-------+---+---+---+---+---+---+---
| 1 | 2 | 2 | 1 | 2 | 1 | 1 ...
+---+---+---+---+---+---+-------+---+---
| 1 | 1 | 2 | 2 | 2 | 2 ...
+---+---+---+---+-------+---+---+---+---
| 2 | 1 | 1 | 2 | 1 | 2 | 1 ...
+---+---+---+---+---+---+---+-------+---
| 1 | 2 | 1 | 1 | 2 | 2 | 1 ...
+---+---+---+---+---+---+---+---+---+---
| 2 | 1 | 1 | 2 | 1 | 1 | 2 ...
+---+---+---+---+---+---+---+---+-------
| 1 | 2 | 1 | 1 | 1 | 2 | 2 ...
+---+-------+---+---+---+---+---+---+---
...
PROG
(C++) See Links section.
CROSSREFS
Cf. A331034.
Sequence in context: A199010 A286944 A026605 * A270646 A293540 A073783
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Jan 09 2020
STATUS
approved