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 A110711 Number of linear arrangements of n blue, n red and n green items such that first and last elements have the same color but there are no adjacent items of the same color. 5
 0, 6, 42, 288, 1992, 13980, 99432, 715344, 5196336, 38056284, 280658100, 2082218160, 15528409920, 116331315360, 874985339760, 6604555554720, 50010373864416, 379760762209692, 2891169309592548, 22062102167330592 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The number of linear arrangements is given by A110706 (first and last elements are not adjacent) and A110707 (first and last elements are adjacent) and the number of circular arrangements (counted up to rotations) is given by A110710. LINKS FORMULA a(n) = 6 * Sum_{k=0..floor(n/2)} binomial(n-1, k) * ( binomial(n-1, k)*binomial(2n-1-2k, n+1) + binomial(n-1, k+1)*binomial(2n-2k-2, n+1) ). a(n) = A110706(n) - A110707(n). a(n) = ((n-3)*A000172(n-1) + n*A000172(n))/(n+1). - Mark van Hoeij, Jul 14 2010 Conjecture: -(n+1)*(n-2)*a(n) + (7*n^2 - 13*n + 4)*a(n-1) + 8*(n-2)^2*a(n-2) = 0. - R. J. Mathar, Nov 01 2015 MAPLE ogf := 6*((x-2)*hypergeom([1/3, 1/3], [1], 27*x^2/((8*x-1)*(x+1)^2)) + 2*hypergeom([1/3, 1/3], [2], 27*x^2/((8*x-1)*(x+1)^2))) / ((1-2* x)*(1+x)^(2/3)*(1-8*x)^(1/3)); series(ogf, x=0, 30); # Mark van Hoeij, Jan 22 2013 PROG (PARI) a(n) = 6 * sum(k=0, n\2, binomial(n-1, k) * ( binomial(n-1, k)*binomial(2*n-1-2*k, n+1) + binomial(n-1, k+1)*binomial(2*n-2*k-2, n+1) )) CROSSREFS Cf. A110706, A110707, A110710. Sequence in context: A242158 A157335 A057089 * A156361 A216517 A055272 Adjacent sequences:  A110708 A110709 A110710 * A110712 A110713 A110714 KEYWORD nonn AUTHOR Max Alekseyev, Aug 04 2005 STATUS approved

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Last modified October 23 20:01 EDT 2019. Contains 328373 sequences. (Running on oeis4.)