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A239572 Triangle T(n, k) = Numbers of non-equivalent (mod D_3) ways to place k points on a triangular grid of side n so that no two of them are adjacent. Triangle read by rows.

%I A239572 #12 Mar 08 2017 11:55:57
%S A239572 1,1,2,2,1,3,6,6,1,4,16,32,24,7,1,5,32,113,200,176,66,6,7,60,329,1053,
%T A239572 1976,2096,1162,302,34,2,8,100,790,3932,12565,25676,32963,25638,11294,
%U A239572 2493,222,7,10,160,1702,11988,57275,187984,425329,658608,684671,462519
%N A239572 Triangle T(n, k) = Numbers of non-equivalent (mod D_3) ways to place k points on a triangular grid of side n so that no two of them are adjacent. Triangle read by rows.
%C A239572 Triangle T(n, k) is irregularly shaped: 1 <= k <= A239438(n). First row corresponds to n = 1.
%C A239572 The maximal number of points that can be placed on a triangular grid of side n so that no two of them are adjacent is given by A239438(n).
%C A239572 Without the restriction "non-equivalent (mod D_3)" numbers are given by A239567.
%H A239572 Heinrich Ludwig, <a href="/A239572/b239572.txt">Table of n, a(n) for n = 1..136</a>
%e A239572 Triangle begins
%e A239572   1;
%e A239572   1;
%e A239572   2,   2,   1;
%e A239572   3,   6,   6,    1;
%e A239572   4,  16,  32,   24,     7,     1;
%e A239572   5,  32, 113,  200,   176,    66,     6;
%e A239572   7,  60, 329, 1053,  1976,  2096,  1162,   302,    34,    2;
%e A239572   8, 100, 790, 3932, 12565, 25676, 32963, 25638, 11294, 2493, 222, 7;
%Y A239572 Cf. A239438, A239567.
%Y A239572 Column 1 is A001399,
%Y A239572 Column 2 is A032091,
%Y A239572 Column 3 is A239573,
%Y A239572 Column 4 is A239574,
%Y A239572 Column 5 is A239575,
%Y A239572 Column 6 is A279446.
%K A239572 nonn,tabf
%O A239572 1,3
%A A239572 _Heinrich Ludwig_, Mar 22 2014