A178284
Number of collinear point 6-tuples in an n X n .. X n 6-dimensional cubical grid.
Original entry on oeis.org
0, 0, 0, 0, 0, 107744, 1861436, 15977216, 92868384, 416136000, 1589753712
Offset: 1
R. H. Hardin, suggested by R. J. Mathar in the Sequence Fans Mailing List, May 24 2010
Three collinear points in an n X n grid
A000938 ; n X n X n grid
A157882
A178285
Number of collinear point 7-tuples in an n X n .. X n 6-dimensional cubical grid.
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 206896, 3575488, 31336956, 188005440, 874477740
Offset: 1
R. H. Hardin, suggested by R. J. Mathar in the Sequence Fans Mailing List, May 24 2010
Three collinear points in an n X n grid
A000938 ; n X n X n grid
A157882
A178288
Number of collinear point 5-tuples in an n X n .. X n 7-dimensional cubical grid.
Original entry on oeis.org
0, 0, 0, 0, 372709, 8494464, 88086873, 587503616, 3369273138, 14491680000, 56179823994, 180939738624, 578688040839, 1597214147200, 4080840158787
Offset: 1
R. H. Hardin, suggested by R. J. Mathar in the Sequence Fans Mailing List, May 24 2010
Three collinear points in an n X n grid
A000938 ; n X n X n grid
A157882
A178289
Number of collinear point triples in an n X n .. X n 8-dimensional cubical grid.
Original entry on oeis.org
0, 0, 192032, 9969920, 455700320, 6065958144, 84525491552, 612465608192, 4331653335264, 21603867355136, 105105371180480, 393780775562496, 1491357451752960, 4669936000634112, 14450643013388864
Offset: 1
R. H. Hardin, suggested by R. J. Mathar in the Sequence Fans Mailing List, May 24 2010
Three collinear points in an n X n grid
A000938 ; n X n X n grid
A157882
A178290
Number of collinear point 4-tuples in an n X n .. X n 8-dimensional cubical grid.
Original entry on oeis.org
0, 0, 0, 807040, 29389312, 406924416, 5493496080, 40707459840, 237337333008, 1379876481024, 6125076674736, 21640203681408, 84999017731696, 274088863846528, 766309629591264
Offset: 1
R. H. Hardin, suggested by R. J. Mathar in the Sequence Fans Mailing List, May 24 2010
Three collinear points in an n X n grid
A000938 ; n X n X n grid
A157882
A178291
Number of collinear point 5-tuples in an n X n .. X n 8-dimensional cubical grid.
Original entry on oeis.org
0, 0, 0, 0, 2687088, 79355392, 1008580720, 7955368960, 55993694000, 284540909568, 1291577484720, 4756123165696
Offset: 1
R. H. Hardin, suggested by R. J. Mathar in the Sequence Fans Mailing List, May 24 2010
Three collinear points in an n X n grid
A000938 ; n X n X n grid
A157882
A178293
Number of collinear point 4-tuples in an n X n .. X n 9-dimensional cubical grid.
Original entry on oeis.org
0, 0, 0, 4907776, 250334405, 4432154880, 83634563315, 797134274560, 5623659900846, 41662871239680, 222405745759290, 917018531400960, 4294168964874715, 16067910057871616, 50983015079601525
Offset: 1
R. H. Hardin, suggested by R. J. Mathar in the Sequence Fans Mailing List, May 24 2010
Three collinear points in an n X n grid
A000938 ; n X n X n grid
A157882
A379299
a(n) is the maximum number k such that every permutation of the integers mod n admits at least k collinear triples.
Original entry on oeis.org
0, 0, 1, 0, 2, 0, 3, 0, 5, 2, 5, 0, 6, 9, 6, 4, 8
Offset: 1
a(5)=2 because the permutation (in one-line notation) 0,1,3,2,4 admits two collinear triples mod 5: {(0,0),(1,1),(4,4)} is on the line y=x and {(0,0),(3,2),(2,3)} is on the line y=4*x; and all other permutations admit at least 2 collinear triples.
- Joshua Cooper and Jack Hyatt, Permutations minimizing the number of collinear triples, arXiv:2501.02331 [math.CO], 2025. See p. 7.
- Joshua N. Cooper and József Solymosi, Collinear points in permutations, Ann. Comb. 9 (2005), no. 2, 169-175; preprint, arXiv:math/0408396 [math.CO], 2004.
- Liangpan Li, Collinear triples in permutations, Innov. Incidence Geom. 8 (2008), 171--173; arXiv preprint, arXiv:0805.0410 [math.CO], 2008.
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