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

0,2

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

Table of n, a(n) for n=0..18.

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