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.

1, 1, 1, 4, 6, 4, 1, 9, 36, 84, 120, 96, 32, 1, 16, 120, 560, 1800, 4128, 6726, 7492, 5238, 1924, 232, 1, 25, 300, 2300, 12600, 52080, 166702, 416622, 808488, 1196196, 1306464, 1001364, 497940, 141336, 18208, 636, 1, 36, 630, 7140, 58800, 373632, 1895938, 7835492

Offset: 1

Author

Heinrich Ludwig, May 07 2014

Keywords

• tabf
• nonn

Comments

The triangle is irregularly shaped: 0 <= k <= A240443(n). The first row corresponds to n = 1.

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).

Examples

			The triangle begins:
  1,  1;
  1,  4,   6,   4;
  1,  9,  36,  84,  120,   96,   32;
  1, 16, 120, 560, 1800, 4128, 6726, 7492, 5238, 1924, 232;
...
		

Links

• Heinrich Ludwig, Table of n, a(n) for n = 1..101

Crossrefs

Cf. A240443, A000290 (column 2), A083374 (column 3), A178208 (column 4), A006857 (column 5 divided by 120), A240445 (column 6), A240446 (column 7).