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A283113 Triangle read by rows: T(n,k) is the number of nonequivalent ways (mod D_3) to place k points on an n X n X n triangular grid so that no two of them are on the same row, column or diagonal (n >= 1).

%I A283113 #12 Sep 12 2019 14:44:43
%S A283113 1,1,1,1,1,2,1,1,3,3,1,1,4,9,5,1,5,19,23,3,1,7,38,82,40,1,1,8,66,230,
%T A283113 242,45,1,10,110,560,1038,533,29,1,12,170,1208,3504,3546,821,6,1,14,
%U A283113 255,2392,9998,16917,9137,807,1,16,365,4405,25158,64345,63755,17408,422
%N A283113 Triangle read by rows: T(n,k) is the number of nonequivalent ways (mod D_3) to place k points on an n X n X n triangular grid so that no two of them are on the same row, column or diagonal (n >= 1).
%C A283113 Length of n-th row is A004396(n) + 1, for 1 <= n <= 21, where A004396(n) is the maximal number of points that can be placed under the condition mentioned above.
%C A283113 Rotations and reflections of placements are not counted. If they are to be counted, see A193986.
%C A283113 In terms or triangular chess: Number of nonequivalent ways (mod D_3) to arrange k nonattacking rooks on an n X n X n board, k>=0, n>=1.
%H A283113 Heinrich Ludwig, <a href="/A283113/b283113.txt">Table of n, a(n) for n = 1..175</a>
%e A283113 The table begins with T(1,0), T(1,1);
%e A283113   1,  1;
%e A283113   1,  1;
%e A283113   1,  2,   1;
%e A283113   1,  3,   3,   1;
%e A283113   1,  4,   9,   5;
%e A283113   1,  5,  19,  23,    3;
%e A283113   1,  7,  38,  82,   40,   1;
%e A283113   1,  8,  66, 230,  242,  45;
%e A283113   1, 10, 110, 560, 1038, 533, 29;
%e A283113   ...
%Y A283113 Row sums give A283117.
%Y A283113 Columns 2..6: A001399, A005994, A283114, A283115, A283116.
%Y A283113 Cf. A004396, A193986.
%K A283113 nonn,tabf
%O A283113 1,6
%A A283113 _Heinrich Ludwig_, Mar 10 2017