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 A090931 Number of permutations of 1,...,2n with alternate odd/even entries that have no adjacent members when placed in a circle. 1

%I

%S 0,0,0,8,140,5940,316708,21536080

%N Number of permutations of 1,...,2n with alternate odd/even entries that have no adjacent members when placed in a circle.

%e The 8 for a(4) are:

%e [7, 4, 1, 6, 3, 8, 5, 2]

%e [5, 2, 7, 4, 1, 6, 3, 8]

%e [1, 4, 7, 2, 5, 8, 3, 6]

%e [3, 8, 5, 2, 7, 4, 1, 6]

%e [3, 6, 1, 4, 7, 2, 5, 8]

%e [5, 8, 3, 6, 1, 4, 7, 2]

%e [1, 6, 3, 8, 5, 2, 7, 4]

%e [7, 2, 5, 8, 3, 6, 1, 4]

%o (PARI) { for (i=1,6, c=0; for (j=1,i!, for (k=1,i!, x=numtoperm(i,j); y=numtoperm(i,k); v=vector(2*i); forstep (z=1,2*i,2, v[z]=x[(z+1)/2]*2-1); forstep (z=2,2*i,2, v[z]=y[z/2]*2); fl=1; for (z=1,2*i-1, if (v[z]==v[z+1]+1, fl=0;break); if (v[z]==v[z+1]-1, fl=0;break)); if (v[2*i]==v[1]+1, fl=0); if (v[2*i]==v[1]-1, fl=0); if (fl==1,c++))); print1(","c)) }

%Y Cf. A092254.

%K nonn

%O 1,4

%A _Jon Perry_, Feb 26 2004

%E a(7)-a(8) from _Alois P. Heinz_, Nov 19 2013

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Last modified December 6 04:20 EST 2021. Contains 349562 sequences. (Running on oeis4.)