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Search: id:A062346
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| A062346 |
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Consider 2n tennis players; a(n) is the number of matches needed to let every possible pair play each other. |
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| 3, 45, 210, 630, 1485, 3003, 5460, 9180, 14535, 21945, 31878, 44850, 61425, 82215, 107880, 139128, 176715, 221445, 274170, 335790, 407253, 489555, 583740, 690900, 812175, 948753, 1101870, 1272810, 1462905, 1673535, 1906128, 2162160, 2443155
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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Number of matchings of size two (edges) in a complete graph on 2n vertices.
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FORMULA
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Superseeker suggests a(n) = (6+25n+35n^2+20n^3+4n^4)/2, but I cannot see why this should be true.
a(n)=n*(4n^3 - 12n^2 + 11n -3)/2. - Swapnil P. Bhatia (sbhatia(AT)cs.unh.edu), Jul 20 2006
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EXAMPLE
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a(2)=3: given players a,b,c,d, the matches needed are (ab,cd), (ac,bd), (ad,bc).
For example, for the K_4 on vertices {0,1,2,3} the possible matchings of size two are: {{0,1}, {2,3}}, {{0,3},{1,2}}, and {{0,2},{1,3}}.
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CROSSREFS
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Sequence in context: A093585 A062270 A069955 this_sequence A002682 A073595 A117972
Adjacent sequences: A062343 A062344 A062345 this_sequence A062347 A062348 A062349
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KEYWORD
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nonn
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AUTHOR
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Michel ten Voorde (seqfan(AT)tenvoorde.org) Jul 06 2001
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EXTENSIONS
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More terms from Swapnil P. Bhatia (sbhatia(AT)cs.unh.edu), Jul 20 2006
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