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

Author

Max Alekseyev, Nov 01 2008

Keywords

• nonn
• hard
• more

Examples

			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]
		

Links

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

Crossrefs

Cf. A135538, A146557.

Programs

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 }

Formula

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

Extensions

Edited by Max Alekseyev, Jun 21 2010

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