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Search: id:A110711
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| A110711 |
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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. |
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6
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| 0, 6, 42, 288, 1992, 13980, 99432, 715344, 5196336, 38056284, 280658100, 2082218160, 15528409920, 116331315360, 874985339760, 6604555554720, 50010373864416, 379760762209692, 2891169309592548, 22062102167330592
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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.
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FORMULA
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a(n) = 6 * Sum[k=0..[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)
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PROGRAM
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(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) ))
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CROSSREFS
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Cf. A110706, A110707, A110710.
Sequence in context: A062310 A105482 A057089 this_sequence A055272 A127628 A111602
Adjacent sequences: A110708 A110709 A110710 this_sequence A110712 A110713 A110714
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KEYWORD
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nonn
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AUTHOR
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Max Alekseyev (maxal(AT)cs.ucsd.edu), Aug 04 2005
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