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Triangular array read by rows in which each term is the least positive integer satisfying the condition that no row, diagonal, or antidiagonal contains a repeated term.
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%I #25 Sep 13 2020 01:58:14

%S 1,2,3,4,4,5,1,2,6,6,7,3,8,4,5,9,8,9,5,6,1,3,7,10,11,10,11,7,12,2,8,5,

%T 6,9,13,14,12,13,9,10,14,7,1,2,15,16,11,8,17,14,15,11,16,12,9,3,4,8,

%U 10,13,17,18,7,19,16,17,13,14,10,11,8,12,1,3,15,9

%N Triangular array read by rows in which each term is the least positive integer satisfying the condition that no row, diagonal, or antidiagonal contains a repeated term.

%C An infinite Sudoku-type array.

%C Here, "diagonal" means a diagonal line with an inclination of -60 degrees, and "antidiagonal" means a diagonal line with an inclination of 60 degrees. Thus, the index-7 cell is in the same row as prior cells of indices 5 and 6, in the same diagonal as prior cells of indices 2 and 6, and in the same antidiagonal as the prior cell of index 4.

%C Triangular tiling is indexed as follows:

%C *

%C / \

%C / 1 \

%C *-----*

%C / \ 3 / \

%C / 2 \ / 4 \

%C *-----*-----*

%C / \ 6 / \ 8 / \

%C / 5 \ / 7 \ / 9 \

%C *-----*-----*-----*

%H Alec Jones, <a href="/A334049/b334049.txt">Table of n, a(n) for n = 1..5000</a>

%e Triangle begins:

%e *

%e / \

%e / 1 \

%e *-----*

%e / \ 3 / \

%e / 2 \ / 4 \

%e *-----*-----*

%e / \ 5 / \ 2 / \

%e / 4 \ / 1 \ / 6 \

%e *-----*-----*-----*

%Y Triangular tiling analog of A269526.

%Y Cf. A274821.

%K nonn,tabf

%O 1,2

%A _Alec Jones_ and _Peter Kagey_, Sep 06 2020