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%I #9 Jun 03 2014 02:31:32
%S 1,1,1,2,4,3,1,3,10,20,25,11,3,4,22,77,186,266,221,86,14,5,41,223,881,
%T 2344,4238,4885,3451,1296,220,7,1,7,72,552,3146,12907,38640,83107,
%U 126701,132236,90214,37128,8235,775,24,8,116,1196,9264,53307,232861,773930
%N Triangle T(n, k) = Numbers of inequivalent (mod D_3) ways to place k points on a triangular grid of side n so that no three of them are vertices of an equilateral triangle with sides parallel to the grid. Triangle read by rows.
%C The triangle T(n, k) is irregularly shaped: 1 <= k <= A227308(n). First row corresponds to n = 1.
%C The maximal number of points that can be placed on a triangular grid of side n so that no three of them form an equilateral triangle with sides parallel to the grid is given by A227308(n).
%H Heinrich Ludwig, <a href="/A243207/b243207.txt">Table of n, a(n) for n = 1..153</a>
%e The triangle begins:
%e 1;
%e 1, 1;
%e 2, 4, 3, 1;
%e 3, 10, 20, 25, 11, 3;
%e 4, 22, 77, 186, 266, 221, 86, 14;
%e 5, 41, 223, 881, 2344, 4238, 4885, 3451, 1296, 220, 7, 1;
%e ...
%e There is T(6, 12) = 1 way to place 12 points (x) on the grid obeying the rule in the definition of the sequence:
%e .
%e x x
%e x . x
%e x . . x
%e x . . . x
%e . x x x x .
%Y Cf. A227308, A243211, A239572, A234247, A231655, A243141, A001399 (column 1), A227327 (column 2), A243208 (column 3), A243209 (column 4), A243210 (column 5).
%K tabf,nonn
%O 1,4
%A _Heinrich Ludwig_, Jun 01 2014
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