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A146558 Number of order n permutations without collinear triples modulo n. 1

%I

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

%N Number of order n permutations without collinear triples modulo n.

%H L. Li, <a href="http://arXiv.org/abs/0802.0572">Collinear triples in permutations</a>, arXiv:0802.0572

%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 hard,more,nonn

%O 1,2

%A _Max Alekseyev_, Nov 01 2008

%E Edited by _Max Alekseyev_, Jun 21 2010

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Last modified February 19 16:02 EST 2019. Contains 320311 sequences. (Running on oeis4.)