A135489 - OEIS

%I #9 Jan 08 2021 20:48:30

%S 1,4,12,42,148,540,1990,7434,27972,106008,403764,1544796,5931486,

%T 22846252,88228998,341518606,1324627044,5146959168,20030812360,

%U 78066774400,304643526276,1190209498344,4654949367204,18223301727108

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

%C 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).

%p 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:

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

%K nonn

%O 0,2

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