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 A137684 Number of tieless (American) football games with n scoring events. 4
 1, 10, 90, 882, 8474, 82650, 803894, 7858034, 76833498, 752970088, 7385132830, 72529933448, 712899726610, 7013548687126, 69048242750358, 680252491600274, 6705715693296522, 66139925760268608, 652678937193274320 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A game is a sequence of valid scores (positive values for the home team, negative values for the visiting team). Note that then the set of valid scores for football is {2,3,6,7,8,-2,-3,-6,-7,-8}. 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 D. Zeilberger, Experimental Mathematics Spring 2008. EXAMPLE a(2)=90, because there are 10^2=100 sequences of length 2 on the alphabet {2,3,6,7,8,-2,-3,-6,-7,-8}; the 10 sequences that correspond to games with ties are precisely those of the form {k,-k}. CROSSREFS Cf. A135490 (basketball). Sequence in context: A033136 A061206 A199527 * A097394 A172199 A063945 Adjacent sequences:  A137681 A137682 A137683 * A137685 A137686 A137687 KEYWORD nonn AUTHOR Sequence discovered by the students of D. Zeilberger's course "Experimental Mathematics", Spring 2008, Rutgers University. Submitted Feb 05 2008 STATUS approved

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Last modified January 24 06:43 EST 2021. Contains 340398 sequences. (Running on oeis4.)