A137684 Number of tieless (American) football games with n scoring events.

1, 10, 90, 882, 8474, 82650, 803894, 7858034, 76833498, 752970088, 7385132830, 72529933448, 712899726610, 7013548687126, 69048242750358, 680252491600274, 6705715693296522, 66139925760268608, 652678937193274320

Offset: 0

Author

Sequence discovered by the students of D. Zeilberger's course "Experimental Mathematics", Spring 2008, Rutgers University. Submitted Feb 05 2008

Keywords

• nonn

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).

Examples

			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}.
		

Links

• D. Zeilberger, Experimental Mathematics Spring 2008.

Crossrefs

Cf. A135490 (basketball).