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Search: id:A135490
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| A135490 |
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Number of tie-less basketball games from the years 1967-present with n scoring events. |
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+0
1
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| 1, 6, 30, 162, 886, 4932, 27714, 157018, 894942, 5126268, 29481732, 170128850, 984577446, 5712117772, 33210790018, 193456179430, 1128789904110, 6596174575548, 38596967873100, 226120320617484, 1326180436400932
(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 1967-present are {1, 2, 3, -1, -2, -3}. 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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LINKS
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D. Zeilberger, Experimental Mathematics Spring 2008.
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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, 3, -1, -2, -3}, n); end:
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CROSSREFS
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Cf. A137684.
Adjacent sequences: A135487 A135488 A135489 this_sequence A135491 A135492 A135493
Sequence in context: A026112 A038155 A026331 this_sequence A110706 A001341 A089896
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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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