A341440 - OEIS

%I #22 Apr 03 2022 22:51:14

%S 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,

%T 13,13,14,6,15,15,16,7,17,8,9,9,18,18,19,10,20,20,21,21,21,22,12,23,

%U 23,24,24,24,14,14,25,15,16,16,26,26,17,17,27,27,28,28

%N 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.

%C 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).

%H Rémy Sigrist, <a href="/A341440/b341440.txt">Table of n, a(n) for n = 0..10200</a>

%H Rémy Sigrist, <a href="/A341440/a341440.png">Colored representation of the tiling</a> (black pixels indicate insertion points, the color is function of the insertion point and the tile orientation)

%H Rémy Sigrist, <a href="/A341440/a341440.gp.txt">PARI program for A341440</a>

%e The spiral begins:

%e       16--15--15---6--14--13--13

%e        |                       |

%e        7   7---6---6---5---5  13

%e        |   |               |   |

%e       17   7   2---2---1   5  12

%e        |   |   |       |   |   |

%e        8   8   2   1---1   4  12

%e        |   |   |           |   |

%e        9   8   3---3---4---4  11

%e        |   |                   |

%e        9   9---3--10--10--11--11

%e        |

%e       18--18--19--10--20--20--21

%o (PARI) See Links section.

%Y See A341291 for another tiling with L trominos.

%K nonn

%O 0,4

%A _Rémy Sigrist_, Feb 12 2021