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A110706
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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.
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8
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6, 30, 174, 1092, 7188, 48852, 339720, 2403588, 17236524, 124948668, 913820460, 6732898800, 49918950240, 372104853600, 2786716100592, 20955408717396, 158149624268220, 1197390368733804, 9091866006950892, 69214297980023256
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The number of circular arrangements is given by A110707 and 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) + binomial(n-1, k+1)*binomial(2n-2k, n+1)) )
a(n) = ((3*n-1)*A000172(n-1)+(3*n+2)*A000172(n))/(n+1)
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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)+binomial(n-1, k+1)*binomial(2*n-2*k, n+1)))
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CROSSREFS
| Cf. A110707, A110710.
Sequence in context: A026331 A135490 A175925 * A001341 A089896 A057754
Adjacent sequences: A110703 A110704 A110705 * A110707 A110708 A110709
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KEYWORD
| nonn
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AUTHOR
| Max Alekseyev (maxale(AT)gmail.com), Aug 04 2005
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