

A235453


Triangle T(n, k) = Number of nonequivalent (mod D_4) ways to arrange k indistinguishable points on an n X n square grid so that no three of them are collinear. Triangle read by rows.


8



1, 0, 1, 2, 1, 1, 3, 8, 13, 15, 5, 1, 3, 21, 70, 181, 217, 142, 28, 4, 6, 49, 290, 1253, 3192, 4699, 3385, 1076, 110, 5, 6, 93, 867, 6044, 27041, 77970, 134353, 129929, 62177, 12511, 717, 11, 10, 171, 2266, 22302, 149217, 672506, 1958674, 3531747, 3695848, 2068757
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OFFSET

1,4


COMMENTS

The triangle T(n, k) is irregularly shaped: 1 <= k <= 2n. First row corresponds to n = 1.
Without the restriction "nonequivalent (mod D_4)" the numbers are given by triangle A194193. (But this one is read by antidiagonals!)
2n is an upper bound on the number of points that can be placed on the grid. For large n, it is conjectured that this bound is not reached (see MathWorld link).


LINKS



EXAMPLE

Triangle begins
1, 0;
1, 2, 1, 1;
3, 8, 13, 15, 5, 1;
3, 21, 70, 181, 217, 142, 28, 4;
6, 49, 290, 1253, 3192, 4699, 3385, 1076, 110, 5;
6, 93, 867, 6044, 27041, 77970, 134353, 129929, 62177, 12511, 717, 11;
...


CROSSREFS



KEYWORD

nonn,tabf


AUTHOR



STATUS

approved



