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A341440
Square spiral of positive integers built by greedy algorithm such that each positive integer appears exactly three times and within a 2 X 2 square area.
1
1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9, 3, 10, 10, 11, 11, 11, 12, 12, 13, 13, 13, 14, 6, 15, 15, 16, 7, 17, 8, 9, 9, 18, 18, 19, 10, 20, 20, 21, 21, 21, 22, 12, 23, 23, 24, 24, 24, 14, 14, 25, 15, 16, 16, 26, 26, 17, 17, 27, 27, 28, 28
OFFSET
0,4
COMMENTS
The motivation for this sequence is to tile a square spiral with L trominoes; for any n > 0, the location of the three occurrences of n correspond to the n-th tile. Graphically, these tiles occupy four periodic regions (see Illustration in Links section).
LINKS
Rémy Sigrist, Colored representation of the tiling (black pixels indicate insertion points, the color is function of the insertion point and the tile orientation)
EXAMPLE
The spiral begins:
16--15--15---6--14--13--13
| |
7 7---6---6---5---5 13
| | | |
17 7 2---2---1 5 12
| | | | | |
8 8 2 1---1 4 12
| | | | |
9 8 3---3---4---4 11
| | |
9 9---3--10--10--11--11
|
18--18--19--10--20--20--21
PROG
(PARI) See Links section.
CROSSREFS
See A341291 for another tiling with L trominos.
Sequence in context: A057366 A371626 A189663 * A355028 A061375 A029920
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Feb 12 2021
STATUS
approved