A135490 Number of tieless basketball games from the years 1967-present with n scoring events.

1, 6, 30, 162, 886, 4932, 27714, 157018, 894942, 5126268, 29481732, 170128850, 984577446, 5712117772, 33210790018, 193456179430, 1128789904110, 6596174575548, 38596967873100, 226120320617484, 1326180436400932

Offset

0,2

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 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).

Links

Table of n, a(n) for n=0..20.

D. Zeilberger, Experimental Mathematics Spring 2008; Local copy, pdf file only, no active links

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, 3, -1, -2, -3}, n); end:

Crossrefs

Cf. A135489 (without 3-pointers), A137684 (American football).

Sequence in context: A026112 A038155 A026331 * A345887 A353891 A353880

Adjacent sequences: A135487 A135488 A135489 * A135491 A135492 A135493

Keyword

nonn

Author

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

Status

approved