

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.


4



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
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OFFSET

1,4


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).


LINKS

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


EXAMPLE

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;
...


CROSSREFS

Cf. A240443, A000290 (column 2), A083374 (column 3), A178208 (column 4), A006857 (column 5 divided by 120), A240445 (column 6), A240446 (column 7).
Sequence in context: A063422 A261638 A010670 * A199358 A131890 A062751
Adjacent sequences: A240441 A240442 A240443 * A240445 A240446 A240447


KEYWORD

tabf,nonn


AUTHOR

Heinrich Ludwig, May 07 2014


STATUS

approved



