

A264801


Number of essentially different seating arrangements for 2n couples around a circular table with 4n seats such that no spouses are neighbors, the neighbors of each person have opposite gender and no person's neighbors belong to the same couple.


1



0, 6, 2400, 6375600, 45927907200, 713518388352000, 21216194909362252800, 1105729617210350356224000, 94398452626533646953922560000, 12514511465855205467497303154688000, 2467490887755897725667792936979169280000
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OFFSET

1,2


COMMENTS

This might be called the "maximum diversity" menage problem. Arrangements that differ only by rotation or reflection are excluded by the following conditions: Seat number 1 is assigned to person A. Seat number 2 can only be taken by a person of the same gender as A. The second condition forces an mmffmmff... pattern.


LINKS

Table of n, a(n) for n=1..11.


FORMULA

a(n) = (2*n1)! * A000183(2*n).


EXAMPLE

a(1)=0 because with 2 couples it is impossible to satisfy all three conditions.
a(2)=6 because only the following arrangements are possible with 4 couples: ABdaCDbc, ABcaDCbd, ACdaBDcb, ACbaDBcd, ADcaBCdb, ADbaCBdc. This corresponds to the (2*21)! possibilities for persons B, C and D to choose a seat. After the positions of A, B, C and D are fixed, only A000183(2*2)=1 possibility remains to arrange their spouses a, b, c and d.


CROSSREFS

Cf. A000183, A007060, A094047, A114939, A258338.
Sequence in context: A198403 A279533 A069643 * A067630 A181700 A199147
Adjacent sequences: A264798 A264799 A264800 * A264802 A264803 A264804


KEYWORD

nonn


AUTHOR

Hugo Pfoertner, Nov 25 2015


STATUS

approved



