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

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

1,2

Links

Table of n, a(n) for n=1..29.

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

Formula

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

Example

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]

Prog

(PARI) { 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 }

Crossrefs

Cf. A135538, A146557.

Sequence in context: A074031 A086261 A111978 * A364514 A025600 A009006

Adjacent sequences: A146555 A146556 A146557 * A146559 A146560 A146561

Keyword

nonn,hard,more

Author

Max Alekseyev, Nov 01 2008

Extensions

Edited by Max Alekseyev, Jun 21 2010

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

Status

approved