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, 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, Table of n, a(n) for n = 0..10200

Rémy Sigrist, Colored representation of the tiling (black pixels indicate insertion points, the color is function of the insertion point and the tile orientation)

Rémy Sigrist, PARI program for A341440

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: A032634 A057366 A189663 * A355028 A061375 A029920

Adjacent sequences: A341437 A341438 A341439 * A341441 A341442 A341443

Keyword

nonn

Author

Rémy Sigrist, Feb 12 2021

Status

approved