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%I #9 Jan 08 2021 20:47:49
%S 1,10,90,882,8474,82650,803894,7858034,76833498,752970088,7385132830,
%T 72529933448,712899726610,7013548687126,69048242750358,
%U 680252491600274,6705715693296522,66139925760268608,652678937193274320
%N Number of tieless (American) football games 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). 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).
%H D. Zeilberger, <a href="http://www.math.rutgers.edu/~zeilberg/math640_08.html">Experimental Mathematics Spring 2008</a>.
%e 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}.
%Y Cf. A135490 (basketball).
%K nonn
%O 0,2
%A Sequence discovered by the students of D. Zeilberger's course "Experimental Mathematics", Spring 2008, Rutgers University. Submitted Feb 05 2008
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