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A235453 Triangle T(n, k) = Number of non-equivalent (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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
The triangle T(n, k) is irregularly shaped: 1 <= k <= 2n. First row corresponds to n = 1.
Without the restriction "non-equivalent (mod D_4)" the numbers are given by triangle A194193. (But this one is read by antidiagonals!)
T(n, 2n) = A000769(n).
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
Eric Weisstein's World of Mathematics, No-Three-in-a-Line-Problem
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
Column 1 is A008805
Column 2 is A014409
Column 3 is A235454
Column 4 is A235455
Column 5 is A235456
Column 6 is A235457
Column 7 is A235458
Sequence in context: A195805 A293908 A346249 * A219206 A077385 A337219
KEYWORD
nonn,tabf
AUTHOR
Heinrich Ludwig, Jan 12 2014
STATUS
approved

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Last modified June 18 11:09 EDT 2024. Contains 373481 sequences. (Running on oeis4.)