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%I #16 Jul 12 2018 00:47:30
%S 1,0,14,90,1114,10718,113216,1152540,11906042,122269186,1258639394,
%T 12943924960,133168371652,1369830663678,14091618522696,
%U 144958402357534,1491181759508514,15339664777115086,157798158205312580,1623258461571800764,16698349602838663718,171774768145224952472
%N Number of tied close American football games: number of ways for the game to have n scoring plays, never be separated by more than one score after each play, and be tied at the end.
%C Each play (counting untimed downs as part of the previous play) can score at most 8 points for one team.
%C The same as counting walks that return to the x-axis of x-length n from the origin bounded above by y=8, below by y=-8, and using the steps {[1,8],..,[1,2],[1,-2],..,[1,-8]}.
%H Bryan Ek, <a href="https://arxiv.org/abs/1803.10920">Lattice Walk Enumeration</a>, arXiv:1803.10920 [math.CO], 2018.
%H Bryan Ek, <a href="https://arxiv.org/abs/1804.05933">Unimodal Polynomials and Lattice Walk Enumeration with Experimental Mathematics</a>, arXiv:1804.05933 [math.CO], 2018.
%F G.f.: (1-4*t-45*t^2-43*t^3+98*t^4+108*t^5-24*t^6-30*t^7)/(1-4*t-59*t^2-77*t^3+170*t^4+234*t^5-92*t^6-142*t^7-4*t^8+6*t^9).
%e There are no tied games with 1 scoring play. To have tied games after 2 scoring plays requires each team to score the same number of points (7 possibilities) in each play (2 orderings): hence 14 walks.
%p taylor((1-4*t-45*t^2-43*t^3+98*t^4+108*t^5-24*t^6-30*t^7)/(1-4*t-59*t^2-77*t^3+170*t^4+234*t^5-92*t^6-142*t^7-4*t^8+6*t^9),t=0,N);
%Y Cf. A300998, A301379, A301381.
%K nonn,walk
%O 0,3
%A _Bryan T. Ek_, Mar 20 2018
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