OFFSET
1,5
COMMENTS
We assume that the chairs are uniform and indistinguishable.
First we arrange the women in alternating seats, in 2*n! ways. Second, we find the number, G_{n} say, of ways of arranging men in the remaining seats such that every husband cannot sit at the left or right next 1, 2, ..., h male's seats from his wife. Note that here h = 2. We give the board B4, where X denotes the seat cannot be set at, where there are h X's in first column, and h+1 X's in first row, ..., 2h X's in the h column, ..., other entries are 1's. Thus the number of different ways to seat a set of n married male-female couples at a straight table is a_{n}=2*n!*G_{n}.
LINKS
Feng Jishe, The board B4
D. Zeilberger, Automatic Enumeration of Generalized Ménage Numbers
D. Zeilberger, Automatic Enumeration of Generalized Menage Numbers, arXiv preprint arXiv:1401.1089 [math.CO], 2014.
FORMULA
a(n) = 2*n! * A292574(n). - Andrew Howroyd, Sep 19 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Feng Jishe, Mar 12 2016
EXTENSIONS
a(11)-a(18) from Andrew Howroyd, Sep 19 2017
STATUS
approved