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 A110707 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). 8
 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; text; internal format)
 OFFSET 1,1 COMMENTS The number of linear arrangements is given by A110706 and the number of circular arrangements counted up to rotations is given by A110710. LINKS 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) - Mark van Hoeij, Jul 14 2010 Conjecture: n^2*a(n) -3*n*(2*n-1)*a(n-1) -3*(n-1)*(5*n-12)*a(n-2) -8*(n-3)^2*a(n-3)=0. - R. J. Mathar, Jul 26 2014 MATHEMATICA b = Binomial; a[n_] := 2*Sum[b[n-1, k]*(b[n-1, k]*(b[2*n+1-2*k, n+1] - 3* b[2*n-1-2*k, n+1]) + b[n-1, k+1]*(b[2*n-2*k, n+1] - 3*b[2*n-2*k-2, n+1]) ), {k, 0, n/2}]; Array[a, 20] (* Jean-François Alcover, Dec 04 2015, adapted from PARI *) 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)) )) CROSSREFS Cf. A110706, A110710, A110711. Sequence in context: A219622 A052170 A027224 * A047712 A188330 A126267 Adjacent sequences:  A110704 A110705 A110706 * A110708 A110709 A110710 KEYWORD nonn AUTHOR Max Alekseyev, Aug 04 2005 STATUS approved

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Last modified October 20 10:45 EDT 2019. Contains 328257 sequences. (Running on oeis4.)