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

0, 0, 0, 8, 140, 5940, 316708, 21536080

Offset

1,4

Links

Table of n, a(n) for n=1..8.

Example

The 8 for a(4) are:
[7, 4, 1, 6, 3, 8, 5, 2]
[5, 2, 7, 4, 1, 6, 3, 8]
[1, 4, 7, 2, 5, 8, 3, 6]
[3, 8, 5, 2, 7, 4, 1, 6]
[3, 6, 1, 4, 7, 2, 5, 8]
[5, 8, 3, 6, 1, 4, 7, 2]
[1, 6, 3, 8, 5, 2, 7, 4]
[7, 2, 5, 8, 3, 6, 1, 4]

Prog

(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)) }

Crossrefs

Cf. A092254.

Sequence in context: A185248 A228867 A224735 * A367199 A376094 A239757

Adjacent sequences: A090928 A090929 A090930 * A090932 A090933 A090934

Keyword

nonn

Author

Jon Perry, Feb 26 2004

Extensions

a(7)-a(8) from Alois P. Heinz, Nov 19 2013

Status

approved