The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 Heinrich Ludwig, Table of n, a(n) for n = 1..99 Achim Flammenkamp, Progress in the no-three-in-line problem 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 Cf. A194193, A000938, A000769. 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 Adjacent sequences: A235450 A235451 A235452 * A235454 A235455 A235456 KEYWORD nonn,tabf AUTHOR Heinrich Ludwig, Jan 12 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

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