%I
%S 1,1,1,4,6,4,1,9,36,84,120,96,32,1,16,120,560,1800,4128,6726,7492,
%T 5238,1924,232,1,25,300,2300,12600,52080,166702,416622,808488,1196196,
%U 1306464,1001364,497940,141336,18208,636,1,36,630,7140,58800,373632,1895938,7835492
%N Triangle T(n, k) = Number of ways to arrange k indistinguishable points on an n X n square grid so that no four of them are vertices of a square of any orientation.
%C The triangle is irregularly shaped: 0 <= k <= A240443(n). The first row corresponds to n = 1.
%C The maximal number of points that can be placed on an n X n square grid so that no four points are vertices of a square is A240443(n).
%H Heinrich Ludwig, <a href="/A240444/b240444.txt">Table of n, a(n) for n = 1..101</a>
%e The triangle begins:
%e 1, 1;
%e 1, 4, 6, 4;
%e 1, 9, 36, 84, 120, 96, 32;
%e 1, 16, 120, 560, 1800, 4128, 6726, 7492, 5238, 1924, 232;
%e ...
%Y Cf. A240443, A000290 (column 2), A083374 (column 3), A178208 (column 4), A006857 (column 5 divided by 120), A240445 (column 6), A240446 (column 7).
%K tabf,nonn
%O 1,4
%A _Heinrich Ludwig_, May 07 2014
