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Search: id:A114939
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| A114939 |
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Number of essentially different seating arrangements for n couples around a circular table with 2*n seats avoiding spouses being neighbors and avoiding clusters of 3 persons with equal gender. |
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+0
4
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| 0, 1, 7, 216, 10956, 803400, 83003040, 11579823360, 2080493573760, 469031859192960, 129727461014726400, 43176116371928601600, 17025803126147196057600, 7850538273249476117913600
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Arrangements that differ only by rotation or reflection are excluded by the following conditions: Seat number 1 is assigned to person (a). Person (a)'s spouse (A) can only take seats with numbers <=(n+1). If (A) gets seat n+1 (i.e. sits exactly opposite to her/his spouse) then person (B) can only take seats with numbers <= n.
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FORMULA
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See PARI code for the formula.
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EXAMPLE
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a(2)=1 because the only valid arrangement is aBAb.
a(3)=7 because the only valid arrangements under the given conditions are: abAcBC, aBAcbC, aBcAbC, aBcACb, acAbCB, acBAbC, aCAbcB.
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PROGRAM
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(PARI) { a(n) = if(n<=1, 0, (-1)^n*(n-1)!*2^(n-1) + n! * polcoeff( polcoeff( [0, 2*y*z^3 + z^2, -3*y*z^5 - 4*z^4 + ((-2*y^2 - 1)/y)*z^3, 6*y*z^7 + (4*y^2 + 11)*z^6 + ((8*y^2 + 4)/y)*z^5 + 3*z^4] * sum(j=0, n-1, j! * [0, 0, 0, -z^6 + z^4; 1, 0, 0, ((y^2 + 1)/y)*z^5 - 2*z^4 + ((-y^2 - 1)/y)*z^3; 0, 1, 0, ((2*y^2 + 2)/y)*z^3 + z^2; 0, 0, 1, -2*z^2]^(n+j) ) * [1, 0, 0, 0]~, 2*n, z), 0, y) / 2 ); }
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CROSSREFS
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Cf. A114938, A137729, A137730, A137737, A137749.
Sequence in context: A061028 A045760 A046033 this_sequence A145107 A140018 A009488
Adjacent sequences: A114936 A114937 A114938 this_sequence A114940 A114941 A114942
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KEYWORD
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nonn
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AUTHOR
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Hugo Pfoertner (hugo(AT)pfoertner.org), Jan 08 2006
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EXTENSIONS
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a(4..7) corrected, formula and further term provided by Max Alekseyev (maxale(AT)gmail.com), Feb 15 2008
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