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

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A059375 Number of seating arrangements for the ménage problem. 6
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.

M. A. Alekseyev, Weighted de Bruijn Graphs for the Menage Problem and Its Generalizations. Lecture Notes in Computer Science 9843 (2016), 151-162. doi:10.1007/978-3-319-44543-4_12 arXiv:1510.07926

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.

Vladimir Shevelev, Peter J. C. Moses, The ménage problem with a known mathematician, arXiv:1101.5321 [math.CO], 2011, 2015.

Wikipedia, Menage Problem

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, A258664, A258665, A258666, A258667, A258673, A259212.

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 | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 5 11:38 EST 2016. Contains 278764 sequences.