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A130810
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If X_1,...,X_n is a partition of a 2n-set X into 2-blocks then a(n) is equal to the number of 4-subsets of X containing none of X_i, (i=1,...,n).
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8
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16, 80, 240, 560, 1120, 2016, 3360, 5280, 7920, 11440, 16016, 21840, 29120, 38080, 48960, 62016, 77520, 95760, 117040, 141680, 170016, 202400, 239200, 280800, 327600, 380016, 438480, 503440, 575360, 654720, 742016, 837760, 942480, 1056720
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OFFSET
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4,1
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COMMENTS
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Number of n permutations (n>=4) of 3 objects u,v,z, with repetition allowed, containing n-4 u's. Example: if n=4 then n-4 =(0) zero u, a(1)=16 because we have vvvv zzzz vvvz zzzv vvzv zzvz vzvv zvzz zvvv vzzz vvzz zzvv vzvz zvzv zvvz vzzv. - Zerinvary Lajos, Aug 05 2008
a(n) is the number of 3-dimensional elements in an n-cross polytope where n>=4. - Patrick J. McNab, Jul 06 2015
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LINKS
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FORMULA
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a(n) = binomial(2*n,4) +binomial(n,2) -n*binomial(2*n-2,2).
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MAPLE
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a:= n-> binomial(2*n, 4) +binomial(n, 2) -n*binomial(2*n-2, 2);
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CROSSREFS
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Cf. A000332, A038207, A000079, A001787, A001788, A001789, A003472, A054849, A002409, A054851, A140325, A140354, A046092, A130809. Equals twice A162668.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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