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A271040
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Number of different 3 against 3 matches given n players.
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1
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0, 0, 0, 0, 0, 0, 10, 70, 280, 840, 2100, 4620, 9240, 17160, 30030, 50050, 80080, 123760, 185640, 271320, 387600, 542640, 746130, 1009470, 1345960, 1771000, 2302300, 2960100, 3767400, 4750200, 5937750, 7362810, 9061920, 11075680, 13449040, 16231600, 19477920
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OFFSET
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0,7
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COMMENTS
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Given n players there are a(n) different ways of arranging those players in a 3 against 3 contest.
Number of ways to select two disjoint subsets of size 3 from a set of n elements. - Joerg Arndt, Mar 29 2016
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LINKS
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FORMULA
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a(n) = n*(n-1)*(n-2)*(n-3)*(n-4)*(n-5)/72.
a(n) = binomial(n,3) * binomial(n-3,3) / 2. - Joerg Arndt, Mar 29 2016
a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7) for n>6.
G.f.: 10*x^6 / (1-x)^7.
(End)
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EXAMPLE
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When there are 6 players, there are 10 different 3 against 3 matches that can be played: ABC v DEF, ABD v CEF, ABE v CDF, ABF v CDE, ACD v BEF, ACE v BDF, ACF v BDE, ADE v BCF, ADF v BCE, AEF v BCD.
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MATHEMATICA
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LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 0, 0, 0, 0, 0, 10}, 40] (* Harvey P. Dale, Sep 17 2016 *)
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PROG
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(PARI) concat(vector(6), Vec(10*x^6/(1-x)^7 + O(x^50))) \\ Colin Barker, Mar 29 2016
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CROSSREFS
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Cf. A050534, the analogous situation for 2 against 2 matches.
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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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