|
%I #12 Mar 18 2020 04:58:32
%S 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
%N Number of order n permutations without collinear triples modulo n.
%H L. Li, <a href="https://arxiv.org/abs/0802.0572">Collinear triples in permutations</a>, arXiv:0802.0572 [math.CO], 2008.
%F For prime p>=3, a(p) = 0.
%e 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]
%o (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 }
%Y Cf. A135538, A146557.
%K nonn,hard,more
%O 1,2
%A _Max Alekseyev_, Nov 01 2008
%E Edited by _Max Alekseyev_, Jun 21 2010
%E a(14)-a(29) from _Bert Dobbelaere_, Mar 15 2020
|
