Search: id:A135490
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%I A135490
%S A135490 1,6,30,162,886,4932,27714,157018,894942,5126268,29481732,170128850,
%T A135490 984577446,5712117772,33210790018,193456179430,1128789904110,
%U A135490 6596174575548,38596967873100,226120320617484,1326180436400932
%N A135490 Number of tie-less basketball games from the years 1967-present with 
               n scoring events.
%C A135490 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).
%H A135490 D. Zeilberger, <a href="http://www.math.rutgers.edu/~zeilberg/math640_08.html">
               Experimental Mathematics Spring 2008</a>.
%p A135490 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 A135490 Cf. A137684.
%Y A135490 Sequence in context: A026112 A038155 A026331 this_sequence A110706 A001341 
               A089896
%Y A135490 Adjacent sequences: A135487 A135488 A135489 this_sequence A135491 A135492 
               A135493
%K A135490 nonn
%O A135490 0,2
%A A135490 Sequence discovered by the students of D. Zeilberger's course (avitalo(AT)math.rutgers.edu), 
               Feb 07 2008

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