A135538 -id:A135538 - cp's OEIS frontend

A179040 Number of permutations of 1..n with no three elements collinear.

1, 1, 2, 4, 18, 56, 272, 1000, 6080, 33644, 214024, 1363836, 10877964, 75783376, 648644300, 5765475224, 49406530846, 431491536076

Offset: 0

R. H. Hardin, including comments and references from R. J. Mathar, Max Alekseyev and Franklin T. Adams-Watters in the Sequence Fans Mailing List, Jun 25 2010

nonn

Number of permutations of 1..n with no three points (i,p(i)) (j,p(j)) (k,p(k)) collinear, or number of n X n permutation matrices with no three 1's collinear.

Dániel T. Nagy, Zoltán Lóránt Nagy, and Russ Woodroofe, The extensible No-Three-In-Line problem, arXiv:2209.01447 [math.CO], 2022.

For "collinear modulo n" see A135538 and A146558.

a(0)=1 prepended by Alois P. Heinz, Sep 14 2022

A146558 Number of order n permutations without collinear triples modulo n.

Original entry on oeis.org

1, 2, 0, 16, 0, 72, 0, 256, 0, 0, 0, 2304, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Max Alekseyev, Nov 01 2008

			For n=4, there are a(4)=16 permutations without collinear triples: [1, 2, 4, 3], [1, 3, 2, 4], [1, 3, 4, 2], [1, 4, 2, 3], [2, 1, 3, 4], [2, 3, 1, 4], [2, 4, 1, 3], [2, 4, 3, 1], [3, 1, 2, 4], [3, 1, 4, 2], [3, 2, 4, 1], [3, 4, 2, 1], [4, 1, 3, 2], [4, 2, 1, 3], [4, 2, 3, 1], [4, 3, 1, 2]

L. Li, Collinear triples in permutations, arXiv:0802.0572 [math.CO], 2008.

Cf. A135538, A146557.

{ a(n) = local(p,r,g); r=0; for(j=1,n!, p=numtoperm(n,j); g=1; forvec(v=vector(3,i,[1,n]), if(matdet([1,v[1],p[v[1]];1,v[2],p[v[2]];1,v[3],p[v[3]]])%n==0, g=0; break), 2); if(g,r++)); r }

For prime p>=3, a(p) = 0.

Edited by Max Alekseyev, Jun 21 2010

a(14)-a(29) from Bert Dobbelaere, Mar 15 2020

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A179040 Number of permutations of 1..n with no three elements collinear.

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A146558 Number of order n permutations without collinear triples modulo n.

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