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A258338 Ternary ménage problem: number of seating arrangements for n opposite-sex couples around a circular table such that no spouses and no triples of the same sex seat next to each other. Seats are labeled. 4
0, 8, 84, 3456, 219120, 19281600, 2324085120, 370554347520, 74897768655360, 18761274367718400, 5708008284647961600, 2072453585852572876800, 885341762559654194995200, 439630143301970662603161600, 251099117378080818090596352000, 163464570058143774978660630528000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Conjecture: (a(n)/n!^2)^(1/n) ~ (3+sqrt(5))/2. - Vaclav Kotesovec, May 29 2015

LINKS

Max Alekseyev, Table of n, a(n) for n = 1..100

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

FORMULA

a(n) = A114939(n) * 4 * n.

PROG

(PARI) { a(n) = if(n<2, 0, n! * sum(j=0, n, (-1)^j * (n-j)! *polcoeff( polcoeff( trace([0, 1, 0, y^2, 0, 0; z*y^2, 0, 1, 0, y^2, 0; z*y^2, 0, 0, 0, y^2, 0; 0, 1, 0, 0, 0, z; 0, 1, 0, y^2, 0, z; 0, 0, 1, 0, y^2, 0]^(2*n)), 2*n, y) , j, z)) ); }

(PARI) { a(n) = if(n<2, 0, n! *  polcoeff( serlaplace( polcoeff( trace([-y, z*y, z, 0, z*y, -y; -y, (z - 1)*y, 0, (z - 1)*y^2, z*y, -y; 0, (z - 1)*y, 0, (z - 1)*y^2, 0, -y; -y, 0, z - 1, 0, (z - 1)*y, 0; -y, z*y, z - 1, 0, (z - 1)*y, -y; -y, z*y, 0, z*y^2, z*y, -y]^n), n, y) )/(1-z) + O(z^(n+1)), n, z) ) }

CROSSREFS

Cf. A114939 (counts up to rotations and reflections)

Cf. A059375, A094047, A000179, A114938, A137729, A137730, A137737, A137749.

Sequence in context: A052659 A113376 A205311 * A245197 A281340 A298283

Adjacent sequences:  A258335 A258336 A258337 * A258339 A258340 A258341

KEYWORD

nonn

AUTHOR

Max Alekseyev, May 27 2015

STATUS

approved

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Last modified November 17 21:07 EST 2018. Contains 317278 sequences. (Running on oeis4.)