A135489 Number of tieless basketball games from the years 1896-1967 with n scoring events.

1, 4, 12, 42, 148, 540, 1990, 7434, 27972, 106008, 403764, 1544796, 5931486, 22846252, 88228998, 341518606, 1324627044, 5146959168, 20030812360, 78066774400, 304643526276, 1190209498344, 4654949367204, 18223301727108

Offset: 0

Author

Sequence discovered by the students of D. Zeilberger's course (avitalo(AT)math.rutgers.edu), Feb 07 2008

Keywords

• nonn

Comments

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 tieless game is one in which the teams are never in a tie (except at the beginning, when no team has scored yet).

Crossrefs

Cf. A135490 (with 3-pointers), A137684 (American football).

Programs

Maple

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: