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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 (list; graph; refs; listen; history; text; internal format)



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.


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


a(n) = (2*n-1)! * A000183(2*n).


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*2-1)! 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.


Cf. A000183, A007060, A094047, A114939, A258338.

Sequence in context: A198403 A279533 A069643 * A067630 A181700 A199147

Adjacent sequences:  A264798 A264799 A264800 * A264802 A264803 A264804




Hugo Pfoertner, Nov 25 2015



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Last modified February 17 23:47 EST 2018. Contains 299297 sequences. (Running on oeis4.)