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Search: id:A135489
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| A135489 |
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Number of tie-less basketball games from the years 1896-1967 with n scoring events. |
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+0
1
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| 1, 4, 12, 42, 148, 540, 1990, 7434, 27972, 106008, 403764, 1544796, 5931486, 22846252, 88228998, 341518606, 1324627044, 5146959168, 20030812360, 78066774400, 304643526276, 1190209498344, 4654949367204, 18223301727108
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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A game is a sequence of valid scores (positive values for the home team, negative values for the visiting team). The valid scores for basketball played during the years 1896-1967 are {1, 2, -1, -2}. A tie-less game is one in which the teams are never in a tie (except at the beginning, when no team has scored yet).
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MAPLE
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TieLessGamesGeneral := proc(S, n, k) local s; option remember; if n = 0 then if k = 0 then return 1; else return 0; fi; fi; if k = 0 then return 0; fi; return add(TieLessGamesGeneral(S, n-1, k-s), s in S); end: TieLessGames := proc(S, n) local k, Smin, Smax; Smin := min(op(S)); Smax := max(op(S)); return add(TieLessGamesGeneral(S, n, k), k = Smin*n..Smax*n); end: TieLessOldBasketballGames := proc(n) return TieLessGames({1, 2, -1, -2}, n); end:
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CROSSREFS
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Cf. A137684.
Sequence in context: A052303 A017942 A149344 this_sequence A100217 A149345 A149346
Adjacent sequences: A135486 A135487 A135488 this_sequence A135490 A135491 A135492
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KEYWORD
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nonn
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AUTHOR
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Sequence discovered by the students of D. Zeilberger's course (avitalo(AT)math.rutgers.edu), Feb 07 2008
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