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A334049 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.

%I A334049 #25 Sep 13 2020 01:58:14
%S A334049 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 A334049 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 A334049 10,13,17,18,7,19,16,17,13,14,10,11,8,12,1,3,15,9
%N A334049 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 A334049 An infinite Sudoku-type array.
%C A334049 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 A334049 Triangular tiling is indexed as follows:
%C A334049            *
%C A334049           / \
%C A334049          / 1 \
%C A334049         *-----*
%C A334049        / \ 3 / \
%C A334049       / 2 \ / 4 \
%C A334049      *-----*-----*
%C A334049     / \ 6 / \ 8 / \
%C A334049    / 5 \ / 7 \ / 9 \
%C A334049   *-----*-----*-----*
%H A334049 Alec Jones, <a href="/A334049/b334049.txt">Table of n, a(n) for n = 1..5000</a>
%e A334049 Triangle begins:
%e A334049            *
%e A334049           / \
%e A334049          / 1 \
%e A334049         *-----*
%e A334049        / \ 3 / \
%e A334049       / 2 \ / 4 \
%e A334049      *-----*-----*
%e A334049     / \ 5 / \ 2 / \
%e A334049    / 4 \ / 1 \ / 6 \
%e A334049   *-----*-----*-----*
%Y A334049 Triangular tiling analog of A269526.
%Y A334049 Cf. A274821.
%K A334049 nonn,tabf
%O A334049 1,2
%A A334049 _Alec Jones_ and _Peter Kagey_, Sep 06 2020