%I #13 Mar 29 2021 13:55:39
%S 1,6,30,162,886,4932,27714,157018,894942,5126268,29481732,170128850,
%T 984577446,5712117772,33210790018,193456179430,1128789904110,
%U 6596174575548,38596967873100,226120320617484,1326180436400932
%N Number of tieless basketball games from the years 1967-present 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 1967-present are {1, 2, 3, -1, -2, -3}. A tieless game is one in which the teams are never in a tie (except at the beginning, when no team has scored yet).
%H D. Zeilberger, <a href="http://www.math.rutgers.edu/~zeilberg/math640_08.html">Experimental Mathematics Spring 2008</a>; <a href="/A135490/a135490.pdf">Local copy, pdf file only, no active links</a>
%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, 3, -1, -2, -3}, n); end:
%Y Cf. A135489 (without 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