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Search: id:A137684
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| A137684 |
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Number of tie-less (American) football games with n scoring events. |
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+0
3
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| 1, 10, 90, 882, 8474, 82650, 803894, 7858034, 76833498, 752970088, 7385132830, 72529933448, 712899726610, 7013548687126, 69048242750358, 680252491600274, 6705715693296522, 66139925760268608, 652678937193274320
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OFFSET
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0,2
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COMMENT
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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 tie-less game is one in which the teams are never in a tie (except at the beginning, when no team has scored yet).
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LINKS
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D. Zeilberger, Experimental Mathematics Spring 2008.
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EXAMPLE
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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}.
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CROSSREFS
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Sequence in context: A003952 A033136 A061206 this_sequence A097394 A063945 A046706
Adjacent sequences: A137681 A137682 A137683 this_sequence A137685 A137686 A137687
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KEYWORD
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nonn
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AUTHOR
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Sequence discovered by the students of Prof. D. Zeilberger's course "Experimental Mathematics", Spring 2008, Rutgers University. Submitted Feb 05 2008
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