cp's OEIS Frontend

A240444 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.

%I A240444 #8 May 09 2014 23:06:29
%S A240444 1,1,1,4,6,4,1,9,36,84,120,96,32,1,16,120,560,1800,4128,6726,7492,
%T A240444 5238,1924,232,1,25,300,2300,12600,52080,166702,416622,808488,1196196,
%U A240444 1306464,1001364,497940,141336,18208,636,1,36,630,7140,58800,373632,1895938,7835492
%N A240444 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 A240444 The triangle is irregularly shaped: 0 <= k <= A240443(n). The first row corresponds to n = 1.
%C A240444 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 A240444 Heinrich Ludwig, <a href="/A240444/b240444.txt">Table of n, a(n) for n = 1..101</a>
%e A240444 The triangle begins:
%e A240444   1,  1;
%e A240444   1,  4,   6,   4;
%e A240444   1,  9,  36,  84,  120,   96,   32;
%e A240444   1, 16, 120, 560, 1800, 4128, 6726, 7492, 5238, 1924, 232;
%e A240444 ...
%Y A240444 Cf. A240443, A000290 (column 2), A083374 (column 3), A178208 (column 4), A006857 (column 5 divided by 120), A240445 (column 6), A240446 (column 7).
%K A240444 tabf,nonn
%O A240444 1,4
%A A240444 _Heinrich Ludwig_, May 07 2014