login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A059375 Number of seating arrangements for the ménage problem. 4
1, 0, 0, 12, 96, 3120, 115200, 5836320, 382072320, 31488549120, 3191834419200, 390445460697600, 56729732529254400, 9659308746908620800, 1905270127543015833600, 431026303509734220288000, 110865322076320374571008000, 32172949121885378686623744000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The "probleme des menages" asks for the number of gender-alternating seating arrangements for n couples around a circular table with the condition that no two spouses are seated adjacently. - Paul C. Kainen and Michael Somos, Mar 11 2011

REFERENCES

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 184, mu*(n).

H. J. Ryser, Combinatorial Mathematics. Mathematical Association of America, Carus Mathematical Monograph 14, 1963, p. 32. equation (2.3).

LINKS

Table of n, a(n) for n=0..17.

Max Alekseyev, On enumeration of seating arrangements of couples around a circular table, Automatic Sequences Workshop, 2015

K. P. Bogart and P. G. Doyle, Nonsexist solution of the menage problem, Amer. Math. Monthly 93:7 (1986), 514-519.

A. Guterman, Pólya permanent problem: 100 years after, 2014.

FORMULA

a(n) = A000179(n) * 2 * n!.

a(n) = A094047(n) * 2 * n.

EXAMPLE

a(3) = 12 because there is a unique seating arrangement up to circular and clockwise / counterclockwise symmetry. - Paul C. Kainen and Michael Somos, Mar 11 2011

PROG

(PARI) {a(n) = local(A); if( n<3, n==0, A = vector(n); A[3] = 1; for(k=4, n, A[k] = (k * (k - 2) * A[k-1] + k * A[k-2] - 4 * (-1)^k) / (k-2)); 2 * n! * A[n])} /* Michael Somos, Mar 11 2011 */

CROSSREFS

Cf. A000179, A258338

Sequence in context: A155620 A219438 A219139 * A251430 A027255 A121791

Adjacent sequences:  A059372 A059373 A059374 * A059376 A059377 A059378

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 28 2001

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified August 2 10:06 EDT 2015. Contains 260198 sequences.