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A110707
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Number of linear arrangements of n blue, n red and n green items such that there are no adjacent items of the same color (first and last elements considered as adjacent).
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6
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6, 24, 132, 804, 5196, 34872, 240288, 1688244, 12040188, 86892384, 633162360, 4650680640, 34390540320, 255773538240, 1911730760832, 14350853162676, 108139250403804, 817629606524112, 6200696697358344, 47152195812692664
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The number of linear arrangements is given by A110706 and the number of circular arrangements counted up to rotations is given by A110710.
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FORMULA
| a(n) = 2 * Sum[k=0..[n/2]] binomial(n-1, k) * ( binomial(n-1, k)*(binomial(2n+1-2k, n+1)-3*binomial(2n-1-2k, n+1)) + binomial(n-1, k+1)*(binomial(2n-2k, n+1)-3*binomial(2n-2k-2, n+1)) )
a(n) = A110706(n) - A110711(n)
a(n) = 2*A000172(n-1)+2*A000172(n) [From Mark van Hoeij (hoeij(AT)math.fsu.edu), Jul 14 2010]
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PROG
| (PARI) a(n) = 2 * sum(k=0, n\2, binomial(n-1, k) * ( binomial(n-1, k)*(binomial(2*n+1-2*k, n+1)-3*binomial(2*n-1-2*k, n+1)) + binomial(n-1, k+1)*(binomial(2*n-2*k, n+1)-3*binomial(2*n-2*k-2, n+1)) ))
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CROSSREFS
| Cf. A110706, A110710, A110711.
Sequence in context: A200160 A052170 A027224 * A047712 A188330 A126267
Adjacent sequences: A110704 A110705 A110706 * A110708 A110709 A110710
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KEYWORD
| nonn
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AUTHOR
| Max Alekseyev (maxale(AT)gmail.com), Aug 04 2005
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